A and B are playing a short game of ping pong where they eac

A and B are playing a short game of ping pong where they each serve twice. If after these four points one of them is ahead by at least two points the game ends, otherwise they go into a second phase. Suppose that A wins 70% of the time when they serve and 40% of the time when B serves. Let

Solution

a) There are 2 marbles numbered 1 and 2 marbles numbered 2

P(The number is odd)

After the first draw we put the marble along with the same number hence result will always be even.

For example first marble is 1 then placed along with 1, sum is 2.

first is 2, placed along with 2, sum is 4.

Hence both even.

II marble: if it is 1, then sum will be either 3 or 5.

Then sum after II draw will be either 2+1+2 =5 or 2+2+3=7

Thus both cases it is odd.

If second marble is 2, then sum after II draw will be either 1+1+2+3 =7 or 2+2+2+4 = 10

a) Prob for sum odd = 1/4 = 0.25

b) Prob (first number was 2 | sum=odd) = 0.5(0.25) =0.125