Question

The Senators have won 75% of the games played against the Canadians over the past few seasons. If this trend continues, what is the probability that the Canadians will win exactly 4 of the next 8 games they play against the Senators this season?

A) 0.035
B) 0.245
C) 0.366
D) 0.488

Answer 1

To find the probability that the Canadians will win exactly 4 of the next 8 games, we can use the binomial probability formula.

Step-by-step explanation:

To find the probability that the Canadians will win exactly 4 of the next 8 games, we need to use the binomial probability formula.

The formula is: P(X = k) = C(n,k) * p^k * (1-p)^(n-k), where:

• P(X = k) is the probability of getting exactly k successes
• C(n,k) is the number of ways to choose k successes from n trials
• p is the probability of success in one trial
• n is the total number of trials
• k is the number of successes

Using the given information, p = 0.25 (since the Canadians win 25% of the games), n = 8, and k = 4.

Plugging these values into the formula, we get:

P(X = 4) = C(8,4) * 0.25^4 * (1-0.25)^(8-4)

Calculating this expression gives us:

P(X = 4) = 70 * 0.25^4 * 0.75^4 = 0.035

Therefore, the probability that the Canadians will win exactly 4 of the next 8 games is 0.035.