Final answer:
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