Question

In a group of 40 students, what is the probability that at most 15 of them like to hike?

Answer 1

To find the probability that at most 15 of the 40 students like to hike, calculate the cumulative probability by summing the individual probabilities. The probability is approximately 0.998.

Step-by-step explanation:

To find the probability that at most 15 of the 40 students like to hike, we need to calculate the cumulative probability.

1. Find the probability that exactly 0 students like to hike by using the binomial probability formula: P(X = 0) = (40 choose 0) * (0.14^0) * (0.86^40) = 0.050
   
2. Find the probability that exactly 1 student likes to hike: P(X = 1) = (40 choose 1) * (0.14^1) * (0.86^39) = 0.149
   
3. Continue this process until finding the probability that exactly 15 students like to hike: P(X = 15) = (40 choose 15) * (0.14^15) * (0.86^25) = 0.237
   
4. Sum up the probabilities for 0 to 15 students: P(X <= 15) = P(X = 0) + P(X = 1) + ... + P(X = 15) = 0.050 + 0.149 + ... + 0.237 = 0.998
   

The probability that at most 15 students like to hike is approximately 0.998.