Chapter 3: Q. 11 (page 215)

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(O).

Short Answer

Expert verified

The solution is $P (O) = \frac{16}{150} = \frac{8}{75} = 0.11$

Step by step solution

Given

Weareprovidedthefollowinginformationinthegivenquestion:

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.

Concept used

Probabilityisametricfordetermininghowcertainweareoftheresultsofacertainexperiment.

Theprobabilityiscalculatedusingthefollowingformula:

Probability

= \frac{Fanorable number of cases}{Total number of cases}

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

Assume that A= only has one tail.

Because localid="1648042298100"

P (A) = \frac{2}{4} = 0.5

, there are two outcomes that favor the event A H T, T H.

Calculation

Calculation:

$∴$ Number of orange jelly beans localid="1648042280499" $= 150 - (22 + 38 + 20 + 28 + 26) = 150$

$- 134 = 16$

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.

Now to find the probability of getting an orange jelly bean, the favorable number of cases is $16$ and total cases are $150$ . Therefore, the probability of getting an orange jelly bean is:

localid="1648042266073" $P (O) = \frac{16}{150} = \frac{8}{75} = 0.11$

Conclusion:

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