Question

Two players, A and B, alternately and independently flip a coin and the firstplayer to obtain a head wins. Assume player A flips first.1. If the coin is fair, what is the probability that A wins?2. Suppose that P(head) = p, not necessarily 12. What is the probability that A wins?

Answer 1

Probability that A wins is 2/3.

Explanation:

player A can win in 2 ways

1) Player A wins immediately by getting head

2) Player A loses immediately by getting tail but wins ultimately as player B gets losses.

a) Probability of 1 to happen is 1/2.

b) Similarly for the event 2 to happen the condition is that A get's a tail and B losses.

Let probability that A wins is 'p' thus we have

`p=P(1)+P(2)\\\\p=(1)/(2)+(1)/(2)* (1-p)\\\\`

Solving for 'p' we get

p= 2/3.