Question

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).

Short answer

The solution is

$$\begin{gathered} P\left(Y\right)=\frac{38}{150} \\ =\frac{19}{75} \\ =0.25 \end{gathered}$$

Step-by-step solution

Given information

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

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

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" $$\begin{gathered} P\left(A\right)=\frac{2}{4} \\ =0.5 \end{gathered}$$, there are two outcomes that favor the event A H T, T H.

Calculation

$\therefore$ Number of orange jelly beans

localid="1651638322634" $$\begin{gathered} =150-(22+38+20+28+26) \\ =150-134 \\ =16 \end{gathered}$$

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" $$\begin{gathered} P\left(Y\right)=\frac{38}{150} \\ =\frac{19}{75} \\ =0.25 \end{gathered}$$