Presentation_ZhouxinShi

Exercise 3.25

Chips in a bag. Imagine you have a bag containing 5 red, 3 blue, and 2 orange chips

1. Suppose you draw a chip and it is blue. If drawing without replacement, what is the probability the next is also blue?

prob<-choose(2, 1)/choose(9, 1)
prob

## [1] 0.2222222

2. Suppose you draw a chip and it is orange, and then you draw a second chip without replacement. What is the probability this second chip is blue?

prob<-choose(3, 1)/choose(9, 1)
prob

## [1] 0.3333333

3. If drawing without replacement, what is the probability of drawing two blue chips in a row?

prob<- (choose(3, 1)/choose(10, 1))*(choose(2, 1)/choose(9, 1))
prob

## [1] 0.06666667

4. When drawing without replacement, are the draws independent? Explain.

• No, the draws are not independent. If we draw without replacement. This changes the probability since we are changing the overall sample space with each draw.