# Probability , kindly solve this question ?

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Sixteen players S1, S2 . . . . . . . . . . . . . . . . . . . S16 play in a tournament. They are divided into eight pairs at random. From each pair a winner is decided on the basis of a game played between the two players of the pair. Assume that all the players are of equal strength:-

(a) Find the probability that the player S1 is among the eight winners.

(b) Find the probability that exactly one of the two players S1 and S2 is among the eight winners.

Sixteen players S1, S2 . . . . . . . . . . . . . . . . . . . S16 play in a tournament. They are divided into eight pairs at random. From each pair a winner is decided on the basis of a game played between the two players of the pair. Assume that all the players are of equal strength:-

(a) Find the probability that the player S1 is among the eight winners.

(b) Find the probability that exactly one of the two players S1 and S2 is among the eight winners.

##### 1 Answer

See below:

#### Explanation:

a) The probability of player ** #1/2#**. This is because the probability of a player (1 person) winning in a pair (2 people) is

In this case, it's:

b) This is a slightly more complex probability question. The probability of just one of

However, also consider the possibility of both S1 and S2 being in the same group. There's only one combination of pairs in which