Question

43​% of men consider themselves professional baseball fans. you randomly select 10 men and ask each if he considers himself a professional baseball fan. find the probability that the number who consider themselves baseball fans is​ (a) exactly​ five, (b) at least​ six, and​ (c) less than four.

Answer 1

To find the probabilities, you can use the binomial probability formula. For (a) exactly 5 men considering themselves baseball fans, calculate P(X=5) using the formula. For (b) at least 6 men, calculate individual probabilities for 6-10 men and add them up. For (c) less than 4 men, calculate individual probabilities for 0-3 men and add them up.

Step-by-step explanation:

To find the probability in each case, we can use the binomial probability formula:

P(X=k) = C(n,k) * p^k * q^(n-k)

Where:

• n is the number of trials (in this case, 10)
• k is the number of successes (in this case, the number of men who consider themselves baseball fans)
• p is the probability of success (0.43)
• q is the probability of failure (1-p)
• C(n,k) is the number of combinations

(a) To find the probability that exactly 5 men consider themselves baseball fans:

P(X=5) = C(10, 5) * (0.43)^5 * (0.57)^5

(b) To find the probability that at least 6 men consider themselves baseball fans, we need to calculate the probabilities of 6, 7, 8, 9, and 10 men considering themselves fans and then add them up:

P(X≥6) = P(X=6) + P(X=7) + P(X=8) + P(X=9) + P(X=10)

(c) To find the probability that less than 4 men consider themselves baseball fans, we need to calculate the probabilities of 0, 1, 2, and 3 men considering themselves fans and then add them up:

P(X<4) = P(X=0) + P(X=1) + P(X=2) + P(X=3)

Answer 2

a)0.43^5*0.57^5

b)0.43^6*0.57^4

c)0.43^3*0.57^7+0.43^2*0.57^8+0.43^1*0.57^9+0.57^10