In a game, each person throws a ball into a bucket. For each person, the random variable X X\,X represents the number of times the ball lands in the bucket in the first 5 throws. Helen models X X\,X as X∼B(5,0.3)X \sim B(5, 0.3)X∼B(5,0.3).
State an assumption Helen makes in order to use her model.
Using Helen's model, find P(X=2)P(X = 2)P(X=2).
For each person, the random variable Y Y\,Y represents the number of the throw on which the ball first lands in the bucket. Using Helen's model, find P(Y=5)P(Y = 5)P(Y=5).