Question

Each game l0 players oot ot every 63 man inc a plover got cno eiko o out of -ine Il gama trs he played.

Answer 1

let X be the random variable denoting the number of games that a player is drug tested.

total games played by the player = 11

probability of getting drug tested = 10/53

thus, X follows a binomial distribution with parameters n = 11 and p = 10/53

to find, P(X=5)

IF X ~ Bin(n,p)

then,

so, $P(X=5) = ^{11}\textrm{C}_5 \times (\frac{10}{53})^5 \times (1-\frac{10}{53})^{11-5}$

or, $P(X=5) = ^{11}\textrm{C}_5 \times (\frac{10}{53})^5 \times (\frac{43}{53})^{6}$