A fair question is tossed 4 times a How many outcomes are th

A fair question is tossed 4 times.

a. How many outcomes are there in the sample space? (show work)

b. What is the probability that the third toss is heads, given that the first toss is heads? (show work)

c. Let A be the event that the first toss is heads, and B be the event that the third toss is heads. Are A and B independent? Why or Why not? (show work)

Solution

a. for every toss there are two possibiities head or tail. so for 4 toss there are 2⁴ = 16 possibilities. so 16 outcomes are there in sample space.

b. toss of third coin does not depend on any previous toss so probability is 1/2.

reason : think of toss as binary no say head = 1 & tell = 0 now toss of 4 coins = 4 digit binary no. now third plece dose not depend on first place of a binary no.

c. A&B are independent because P(A) * P(B) = P(AB) [(1/2)*(1/2) = 1/4]