Question

There are 5 Snickers, 10 Baby Ruths, 13 Milky Ways, 12 Twixs and17 Almond Joys in a bowl of candy. You reach into the bowl and randomly select 5 candy bars. Use this information to answer the next two questions. What is the probability you select exactly 2 Milky Way bars?

Answer 1

Answer: 0.2415

Explanation:

Given : There are 5 Snickers, 10 Baby Ruths, 13 Milky Ways, 12 Twixs and17 Almond Joys in a bowl of candy.

Total candy bars :
`5+10+13+12+17=57`

Probability of getting a Milky Way bar=
`p=\frac{\text{No. of Milky bars}}{\text{Total candy bars}}`

`\Rightarrrow\ p=(13)/(57)\approx0.23`

Using Binomial distribution , the probability of getting success in x trials is given by:-

`P(x)=^nC_xp^x(1-p)^(n-x)`, where p uis probability of success in each trial and n is sample size.

If you randomly select n= 5 candy bars, then the probability you select exactly 2 Milky Way bars Will be :_

`P(2)=^5C_2(0.23)^2(1-0.23)^(3)\\\\=(5!)/(2!(5-2)!)(0.23)^2(0.77)^3\\\\=0.241505957\approx0.2415`

Hence, the probability you select exactly 2 Milky Way bars = 0.2415