Question

A. Twenty-six percent of couples who plan to massy this year are planning a destination wedding. A sample of 4 couples who plan to marry is selected, find the probability that: At least 2 couples will have a destination wedding. b. Exactly 2 couples will have a destination wedding. Fewer than 3 couples will have a destination wedding. C. Select one or more:

0.943
0.225
0.279
0.995
0.222
b. How many ways can an adviser choose 3 students from a class of so if they are all given the same task? O a. 1000 Ob. 720 Oc. 210 O d. 120

Answer 1

To find the probability that at least 2 couples will have a destination wedding, use the binomial probability formula.

Step-by-step explanation:

To find the probability that at least 2 couples will have a destination wedding, you can use the binomial probability formula. The formula is P(X >= k) = 1 - P(X < k), where X is the number of couples having a destination wedding and k is the desired number of couples. Let's calculate it step-by-step:

P(X >= 2) = 1 - P(X < 2)

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

P(X = 0) = (0.26)^0 * (1 - 0.26)^(4-0) = 0.3145

P(X = 1) = (0.26)^1 * (1 - 0.26)^(4-1) * 4 = 0.4034

P(X < 2) = 0.3145 + 0.4034 = 0.7179

P(X >= 2) = 1 - 0.7179 = 0.2821.

Answer 2

a. Probability that at least 2 couples will have a destination wedding is approximately 0.5624. b. Probability that exactly 2 couples will have a destination wedding is approximately 0.3439. c. Probability that fewer than 3 couples will have a destination wedding is approximately 0.4869.

Step-by-step explanation:

a. Probability that at least 2 couples will have a destination wedding:

To find this probability, we need to calculate the probability of 2, 3, and 4 couples having a destination wedding and then sum them up.

Probability of 2 couples having a destination wedding:

P(2) = C(4, 2) * (0.26)^2 * (0.74)^2 ≈ 0.3439

Probability of 3 couples having a destination wedding:

P(3) = C(4, 3) * (0.26)^3 * (0.74) ≈ 0.2009

Probability of 4 couples having a destination wedding:

P(4) = C(4, 4) * (0.26)^4 * (0.74)^0 ≈ 0.0176

Now, we can sum up these probabilities to get the probability of at least 2 couples having a destination wedding:

P(at least 2) = P(2) + P(3) + P(4) ≈ 0.3439 + 0.2009 + 0.0176 ≈ 0.5624

b. Probability that exactly 2 couples will have a destination wedding:

P(exactly 2) = C(4, 2) * (0.26)^2 * (0.74)^2 ≈ 0.3439

c. Probability that fewer than 3 couples will have a destination wedding:

P(fewer than 3) = P(0) + P(1) + P(2) = (0.74)^4 + C(4, 1) * (0.26)^1 * (0.74)^3 + P(2) ≈ 0.4869