Question

A and B are equally good tennis players. Which of the following two events is more probable?
(i) A beats B exactly in 3 games out of 4.
(ii) A beats B exactly in 5 games out of 8.

Answer 1

event B is more probable as both are equally good so there chance of winning is 50-50.in first case the percentage goes to 75 for A which is quite more than what it should be, but in second case the percentage for A is approx 60 so it can happen

Answer 2

Since both are good players p(a) = p(b) = 1/2 = 0.5

(1) Probability of A beats B exactly in 3 games out of 4 = 4c3 * (0.5)^3 * (0.5)^1

                                                                                            = 4c1 * (0.5)^4
  
                                                                                            = 4 * 0.0625

                                                                                            = 0.25.


(2) Probability of A beats B exactly in 5 games out of 8 = 8c5 * (0.5)^5 * (0.5)^3
                 
                                                                                             = 8c3 * (0.5)^8

                                                                                             = 0.21.


From (1) and (2), We can say that 1st event is more probable.


Hope this helps!