Question

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(B).

Short answer

$P\left(B\right)=\frac{26}{150}=\frac{13}{75}=0.17$

Step-by-step solution

Given Information

In the given question, we are given the following information:

A jar of 150 jelly beans contains 22 red jelly beans, 38 yellow, 20 green, 28 purple, 26 blue and the rest are orange.

Concept Used

Probability is a measure that is associated with how certain we are of outcomes of a particular experiment.

The formula for calculating the probability is:

Probability $=\frac{\text{Favrable number of cases}}{\text{Total number of cases}}$

For example, if we flip a coin two times, the sample space associated with this random experiment is $\{HH,HT,TH,TT\}$where T= tails and H= heads. Let's suppose A= getting one tail. There are two

outcomes which favors the event A

$\{HT,TH\}$, so $P\left(A\right)=\frac{2}{4}=0.5$.

Calculation

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

$=-134$

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 a blue jelly bean, the favorable number of cases is 26 and total cases are 150 . Therefore, the probability of getting a blue jelly bean is:

$P\left(B\right)=\frac{26}{150}=\frac{13}{75}=0.17$

Conclusion

$P\left(B\right)=0.17.$