a Suppose that PA1 or A2 or A3 or A4 or A5 or A6 04 PA1 or

a) Suppose that  P(A1 or A2 or A3 or A4 or A5 or A6) = 0.4   

P(A1 or A2)=0.31  

P(A3 or A4)=0.07

then what is P(A5 or A6)?

b) Suppose you flip a coin, which was randomly selected from a bag of two coins - one with two heads and the other with a head and tail. What is the probability that it comes up as heads?

Thank you

Solution

1) as nothing is mentioned we assume that the Ai\'s are mutually exclusive

therefore P = 0.4 = P( A1 or A2) + P( A3 or A4) + P( A5 or A6)

implies P( A5 or A6) = 0.4 - 0.31 - 0.07 = 0.02

2) P (head) = P( first coin and head) + P( second coin and head) = 0.5*1 + 0.5*0.5 = 0.5 + 0.25 = 0.75