In the 2016-17 NHL season, Sidney Crosby scored on 24% of his shots. If he takes
ID: 3253379 • Letter: I
Question
In the 2016-17 NHL season, Sidney Crosby scored on 24% of his shots. If he takes 10 shots in one game, what is the probability he records a hat trick (exactly 3 goals)? Assume shots are independent? b. In 1941, Ted Williams finished the baseball season getting hits on 40.6% of his at-bats (the last player to bat .400 in a full season.) If he got 5 at-bats in one game, what is the probability of him getting at least 4 hits? c. Hope Solo's save percentage throughout her soccer career is 77.6%. If she faces 4 shots in one game, what is the probability that she records a shutout (i.e. allows zero goals)?Explanation / Answer
a. Let X be the random variable denoting the number of goals scored by him.
X ~ Bin (n,p) where n = 10, p = 0.24.
Hence probability of scoring a hat-trick = P(X=3) = 0.2429. (Ans).
b. Let Y be the random variable denoting the number of hits.
Y ~ Bin (5, 0.406)
Required probability = P(Y=4) = 0.0807. (Ans).
c. Let Z be the random variable denoting the number of days she allowed.
Z ~ Bin (4, 0.776)
Hence the required probability = P(Z=0) = 0.0025. (Ans).