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(O).

Short answer

The solution is$$\begin{gathered} P\left(O\right)=\frac{16}{150} \\ =\frac{8}{75} \\ =0.11 \end{gathered}$$

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

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

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

Assume that A= only has one tail.

Because localid="1648042298100" $$\begin{gathered} P\left(A\right)=\frac{2}{4} \\ =0.5 \end{gathered}$$, there are two outcomes that favor the event A H T, T H.

Calculation

Calculation:

$\therefore$Number of orange jelly beans localid="1648042280499" $$\begin{gathered} =150-(22+38+20+28+26) \\ =150 \end{gathered}$$

$-134=16$

Let B= the event of getting a blue jelly bean

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

Let $\mathrm{O}=$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" $$\begin{gathered} P\left(O\right)=\frac{16}{150} \\ =\frac{8}{75} \\ =0.11 \end{gathered}$$

Conclusion: