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Q.10

Expert-verifiedFound in: Page 215

Book edition
OER 2018

Author(s)
Barbara Illowsky, Susan Dean

Pages
902 pages

ISBN
9781938168208

Use the following information to answer the next six exercises. A jar of $150$ jelly beans contains $22$ red jelly beans, $38$

yellow, $20$ green, $28$ purple, $26$ blue, and the rest are orange.

Let B = the event of getting a blue jelly bean

Let G = the event of getting a green jelly bean.

Let O = the event of getting an orange jelly bean.

Let P = the event of getting a purple jelly bean.

Let R = the event of getting a red jelly bean.

Let Y = the event of getting a yellow jelly bean.

Find P(Y).

The solution is

$P\left(Y\right)=\frac{38}{150}\phantom{\rule{0ex}{0ex}}=\frac{19}{75}\phantom{\rule{0ex}{0ex}}=0.25$We are provided the following information in the given question:

$22$ red jelly beans,$38$ yellow jelly beans, $20$ green jelly beans, $28$ purple jelly beans, $26$ blue jelly beans, and the rest are orange jelly beans make up a jar of $150$ jelly beans.

Probability is a metric for determining how certain we are of the results of a certain experiment.

The probability is calculated using the following formula:

Probability

$=\frac{\text{Farorable number of cases}}{\text{Total number of cases}}$

If we flip a coin twice, the sample space associated with this random experiment is H, H T, T H, T T, where T= tails and H= heads.

Let's say A= only has one tail.

Because localid="1648041984677" $P\left(A\right)=\frac{2}{4}\phantom{\rule{0ex}{0ex}}=0.5$, there are two outcomes that favor the event A H T, T H.

$\therefore $ Number of orange jelly beans

localid="1651638322634" $=150-(22+38+20+28+26)\phantom{\rule{0ex}{0ex}}=150-134\phantom{\rule{0ex}{0ex}}=16$Let B= the event of getting a blue jelly bean

Let $\mathrm{G}=$ the event of getting a green jelly bean.

Let O= the event of getting an orange jelly bean.

Let P= the event of getting a purple jelly bean.

Let R= the event of getting a red jelly bean.

Let Y= the event of getting a yellow jelly bean.

Now to find the probability of getting a yellow jelly bean, the favorable number of cases is $38$ and total cases are 150 . Therefore, the probability of getting a yellow jelly bean is:

localid="1648042037831" $P\left(Y\right)=\frac{38}{150}\phantom{\rule{0ex}{0ex}}=\frac{19}{75}\phantom{\rule{0ex}{0ex}}=0.25$

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