Question

if the probability is .05 that a baseball game will go into an extra inning, find the probabilities that among 15 baseball games a. exactly one will go into extra inning; b. at most 2 will go into extra innings; c. at least 2 will go into extra innings.

Answer 1

To find the probabilities, we can use the binomial probability formula: P(X = k) = (nCk) * p^k * (1-p)^(n-k), where P(X = k) is the probability of exactly k successes, n is the number of trials (in this case, 15), k is the number of successes we're interested in (exactly one, at most two, or at least two), and p is the probability of success (0.05).

Step-by-step explanation:

To find the probabilities, we can use the binomial probability formula:

P(X = k) = (nCk) * p^k * (1-p)^(n-k)

where:

• P(X = k) is the probability of exactly k successes
• n is the number of trials (in this case, 15)
• k is the number of successes we're interested in (exactly one, at most two, or at least two)
• p is the probability of success (0.05)

a. Exactly one will go into extra inning:

P(X = 1) = (15C1) * (0.05)^1 * (0.95)^(15-1)

P(X = 1) = 15 * 0.05 * 0.95^14

b. At most two will go into extra innings:

P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)

P(X ≤ 2) = (15C0) * (0.05)^0 * (0.95)^15 + (15C1) * (0.05)^1 * (0.95)^14 + (15C2) * (0.05)^2 * (0.95)^13

c. At least two will go into extra innings:

P(X ≥ 2) = 1 - P(X < 2)

P(X < 2) = P(X = 0) + P(X = 1)

P(X ≥ 2) = 1 - (P(X = 0) + P(X = 1))