Intermediate Mathematics

Predicting Outcomes

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Predicting Outcomes
You can use probability to predict the number of times an event will occur.
A number cube has faces labeled 1 through 6. Suppose you roll this cube 30 times. How many times can you expect to roll an odd number?
On a single roll, the probability of rolling an odd number (1, 3, or 5) is 3 out of 6, or\(\frac{1}{2}\) in simplest form.
\(\frac{1}{2} × 30 = 15\)
If the cube is rolled 30 times, you can expect to roll an odd number about 15 times. This number, of course, is just a prediction. The actual count of odd numbers on 30 random rolls could be more or less than 15.
Predicting Outcomes
To predict the number of times an event will occur, multiply the probability of the event by the number of attempts.
There are 210 students enrolled at Elm Street School. Predict the number of those students who were born on a Saturday.
Since there are 7 days in a week, the probability of a person being born on a Saturday is\(\frac{1}{7}\).
\(\frac{1}{7} × 210 = 30\)
The prediction is that about 30 of the Elm Street School students were born on a Saturday.
Predicting Outcomes
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If you flip a coin 50 times, about how many times can you expect the coin to land on "heads"?
25
50
0
10
None of these
Question 1 of 8
P(heads) = \(\color{#0a7d0a}{\frac{1}{2}}\)
\[\frac{1}{2} × 50 = 25\]
You can predict that the coin will land on "heads" about 25 times.
It would be very unusual for the coin to land on "heads" every time. The probability of "heads" is\(\color{#be0a0a}{\frac{1}{2}}\) on each flip. Try again.
It would be very unusual for the coin never to land on "heads." The probability of "heads" is \(\color{#be0a0a}{\frac{1}{2}}\) on each flip. Try again.
While it is possible for the coin to land on "heads" 10 times, there is a better prediction. The probability of "heads" is\(\color{#be0a0a}{\frac{1}{2}}\) on each flip. Try again.
One of these is a good prediction. Try again.
To predict the number of times an event will occur, multiply the probability of the event by the number of attempts.
Predicting Outcomes
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Your company employs 480 people. Predict the number of employees who were born in May. (Assume there is equal probability for each month of the year.)
400
48
40
12
None of these
Question 2 of 8
It would be very unlikely that 400 people would be born in May. The probability of being born in May is\(\color{#be0a0a}{\frac{1}{12}}\) for each person. Try again.
While it is possible for 48 people to be born in May, there is a better prediction. The probability of being born in May is \(\color{#be0a0a}{\frac{1}{12}}\) for each person. Try again.
P(May) = \(\color{#0a7d0a}{\frac{1}{12}}\)
\(\color{#0a7d0a}{\frac{1}{12} × 480 = 40}\)
You can predict that about 40 employees were born in May.
While it is possible for 12 people to be born in May, there is a better prediction. The probability of being born in May is\(\color{#be0a0a}{\frac{1}{12}}\) for each person. Try again.
One of these is a good prediction. Try again.
To predict the number of times an event will occur, multiply the probability of the event by the number of attempts.
Predicting Outcomes
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There are 8 chips in a bag, and only 2 of them are red. Each time you draw a chip out of the bag, you record your selection and place the chip back into the bag. If you made 20 selections, predict how many times you can expect to draw a red chip.
20
5
2
40
None of these
Question 3 of 8
It would be very unusual to pull out a red chip every time. The probability of picking a red chip is \(\color{#be0a0a}{\frac{1}{4}}\) on each try. Try again.
P(red) = \(\color{#0a7d0a}{\frac{2}{8}}\) or \(\color{#0a7d0a}{\frac{1}{4}}\)
\(\color{#0a7d0a}{\frac{1}{4} × 20 = 5}\)
You can predict that you will draw a red chip about 5 times.
There are 2 red chips in the bag. The probability of picking a red chip is \(\color{#be0a0a}{\frac{1}{4}}\) on each try. Try again.
You are only going to make 20 selections from the bag, so it would be impossible to draw a red chip 40 times. Try again.
One of these is a good prediction. Try again.
To predict the number of times an event will occur, multiply the probability of the event by the number of attempts.
Predicting Outcomes
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If you spin the pointer 100 times, about how many times can you expect it to land on a number less than 3?
2
100
0
25
None of these
Question 4 of 8
There are two numbers on the spinner less than 3. The probability of the pointer landing on 1 or 2 is\(\color{#be0a0a}{\frac{2}{8}}\) for each spin. Try again.
It would be very unusual for the pointer never to land on 1 or 2. The probability of the pointer landing on 1 or 2 is \(\color{#be0a0a}{\frac{2}{8}}\) for each spin. Try again.
It would be very unusual for the pointer never to land on 1 or 2. The probability of the pointer landing on 1 or 2 is \(\color{#be0a0a}{\frac{2}{8}}\) for each spin. Try again.
P(1 or 2) = \(\color{#0a7d0a}{\frac{2}{8}}\) or \(\color{#0a7d0a}{\frac{1}{4}}\)
\(\color{#0a7d0a}{\frac{1}{4}}\) × 100 = 25 You can predict that the pointer will land on a number less than 3 about 25 times.
One of these is a good prediction. Try again.
To predict the number of times an event will occur, multiply the probability of the event by the number of attempts.
Predicting Outcomes
To predict the number of times an event will occur, multiply the probability of the event by the number of attempts.
There are 5 different kinds of stickers used to make bookmarks in 4 different colors. How many red bookmarks with star stickers would you expect to find in a stack of 100 bookmarks?
There are 5 different stickers.
There are 4 colors.
5 x 4 = 20

There are 20 different bookmarks.
P(red with star) = \(\frac{1}{20}\)
\(\frac{1}{20} × 100 = 5\)

You would expect 5 of the bookmarks to be red with star stickers.
Predicting Outcomes
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On Potluck Pasta Night at the fire hall, they serve 5 types of pasta and 2 kinds of sauces, but you don't know which kind of pasta and sauce you'll get. If you go to Potluck Pasta Night 80 times, about how many times do you think you'll get linguine with meat sauce?
10
2
5
40
None of these
Question 5 of 8
There are 10 possible combinations of pastas and sauces. The probability of getting linguine and meat sauce is\(\color{#be0a0a}{\frac{1}{10}}\) for each visit. Try again.
There are 5 x 2, or 10, combinations of pastas and sauces. The probability of getting linguine and meat sauce is \(\color{#be0a0a}{\frac{1}{10}}\) for each visit. Try again.
There are 5 x 2, or 10, combinations of pastas and sauces. The probability of getting linguine and meat sauce is \(\color{#be0a0a}{\frac{1}{10}}\) for each visit. Try again.
There are 5 x 2, or 10, combinations of pastas and sauces. The probability of getting linguine and meat sauce is \(\color{#be0a0a}{\frac{1}{10}}\) for each visit. Try again.
Possible outcomes: 5 x 2 = 10
\(\color{#0a7d0a}{\frac{1}{10} × 80 = 8}\)
You can predict that you'll get linguine with meat sauce about 8 times.
To predict the number of times an event will occur, multiply the probability of the event by the number of attempts.
Predicting Outcomes
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Each day, Cindy's Coffee Shop labels one of its 15 coffees the surprise Coffee of the Day. The shop serves its coffee in 2 different mugs. Predict how many times you will be served hazelnut coffee in a black mug over a 180-day period.
30
180
6
2
None of these
Question 6 of 8
There are 30 possible combinations of coffees and mugs. The probability of getting hazelnut coffee in a black mug is\(\color{#be0a0a}{\frac{1}{30}}\) for each visit. Try again.
There are 15 x 2, or 30, combinations of coffees and mugs. The probability of getting hazelnut coffee in a black mug is \(\color{#be0a0a}{\frac{1}{30}}\) for each visit. Try again.
Possible outcomes: 15 x 2 = 30 \(\color{#0a7d0a}{\frac{1}{30} × 180 = 6}\)
You can predict that you'll get hazelnut coffee in a black mug about 6 times.
There are 15 x 2, or 30, combinations of coffees and mugs. The probability of getting hazelnut coffee in a black mug is\(\color{#be0a0a}{\frac{1}{30}}\) for each visit. Try again.
One of these is a good prediction. Try again.
To predict the number of times an event will occur, multiply the probability of the event by the number of attempts.
Predicting Outcomes
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Wendy has 6 different shirts and 5 different pairs of shorts that she wears to the gym. Predict the number of times Wendy will wear her green shirt with her black shorts if she pulls a shirt and pair of shorts at random for each of 120 visits to the gym.
0
4
100
120
None of these
Question 7 of 8
It would be very unusual for Wendy never to wear this combination. The probability of Wendy wearing this combination is\(\color{#be0a0a}{\frac{1}{30}}\) for each visit. Try again.
Possible outcomes: 6 x 5 = 30
\(\color{#0a7d0a}{\frac{1}{30} × 120 = 4}\)
It is likely that Wendy will wear the green shirt and black shorts about 4 times.
There are 6 x 5, or 30, combinations of shirts and shorts. The probability of Wendy wearing this combination is \(\color{#be0a0a}{\frac{1}{30}}\) for each visit. Try again.
It would be very unusual for Wendy always to wear this combination. The probability of Wendy wearing this combination is \(\color{#be0a0a}{\frac{1}{30}}\) for each visit. Try again.
One of these is a good prediction. Try again.
To predict the number of times an event will occur, multiply the probability of the event by the number of attempts.
Predicting Outcomes
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Each box of 1,000 paper clips is filled randomly with 2 different sizes and 10 different colors. Predict the number of small, red paper clips in a box.
100
50
500
20
None of these
Question 8 of 8
There are 2 x 10, or 20, combinations of sizes and colors. The probability of a paper clip being small and red is \(\color{#be0a0a}{\frac{1}{20}}\). Try again.
Possible outcomes: 10 x 2 = 20
\(\color{#0a7d0a}{\frac{1}{20}}\) × 1000 = 50
You can predict that 50 of the paper clips will be small and red.
There are 2 x 10, or 20, combinations of sizes and colors. The probability of a paper clip being small and red is \(\color{#be0a0a}{\frac{1}{20}}\). Try again.
There are 20 combinations of sizes and colors. The probability of a paper clip being small and red is \(\color{#be0a0a}{\frac{1}{20}}\). Try again.
One of these is a good prediction. Try again.
To predict the number of times an event will occur, multiply the probability of the event by the number of attempts.
Predicting Outcomes