Question

PLEASE DON’T COPY PASTE FEOM PREVIOUS QUESTION

1)On Planet Geometry, whenever two right angles have children they can have rectangles or squares with equal probability each. Consider a (very nice) pair of right angles that have 2 children.

a) Using a tree diagram, what is the probability that both children are squares given that at least one is a square? (It is not 1⁄2!)

2) Suppose that P(A∩B)=.3,P(A)=.6, and P(B)=.5.

a. Are A and B mutually exclusive?
b. Are A and B independent?

Answer 1

1) Consider the tree diagram given below

P(both children are squares | at least one is a square) = P(both children are squares) / P(at least one is a square)

= P(both children are squares) / [1 - P(both children are rectangles)]

= 0.5x0.5 / (1 - 0.5x0.5)

= 2/3

2) P(A) = 0.6

P(B) = 0.5

P(A B) = 0.3

a. If two events A and B are mutually exclusive, P(A B) = 0

Here, P(A B) 0 and hence, the events are not mutually exclusive.

b. If A and B are independent, P(A) x P(B) = P(A B)

Here, P(A) x P(B) = 0.6 x 0.5 = 0.3

P(A B) = 0.3

P(A) x P(B) = P(A B)

Therefore, A and B are independent.