Question

Tyler is offered to choose between three boxes that look identical. The first box contains 1 red pills and 19 blue pills, the second box has 6 red pills and 14 blue pills, and the third box has 2 red pills and 18 blue pills. Tyler randomly picks a box and takes one pill out.
a. Find the likelihood that the pill will be red?
b. Tyler randomly picks a box and takes 11 pills out. Find the likelihood that he will get 1 red pills and 10 blue pills

Answer 1

Answer:

A) 0.15

B) 0.36

Step-by-step explanation:

First Box consist 1 red pills and 19 blue pills

second box consist 6 red pills and 14 blue pills

Third box consist 2 red pills and 18 blue pills

a) Prob ( randomly chosen pill is red) $= \frac{1}{3} \times \frac{1}{20} + \frac{1}{3} \times \frac{6}{20} + \frac{1}{3} \times \frac{2}{20}$

$\frac{1}{60} (1+6+2) = 0.15$

b)Prob ( 1 reds and 10 blue pilss) =$\frac{1}{3} \frac{^1C_1\times ^{19}C_{10}}{^{20}C_{11}} + \frac{1}{3} \frac{^6C_1\times ^{14}C_{10}}{^{20}C_{11}} + \frac{1}{3} \frac{^2C_1\times ^{18}C_{10}}{^{20}C_{11}}$

$= \frac{1}{3} 1.106 = 0.368$