Question

The probability that Pete will catch fish when he goes fishing is 0.84. Pete is going to fish 3 days next week. Define the random variable x to be the number of days Pete catches fish. What is the probability that Pete will catch fish on one day or less?

0.065

0.069    

0.840

0.935

Answer 1

Let X be a number of days that Pete will catch fish among 3 days next week. P(catching a fish) = p = 0.84

Here, X ~ Binomial (n = 3, p = 0.84)

We want to find, the probability that Pete will catch fish on one day or less. That is to find, P(X ≤ 1)

P(X ≤ 1)

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

= [ 3C0 * (0.84)0 * (1 - 0.84)3-0 ] + [ 3C1 * (0.84)1 * (1 - 0.84)3-1 ]

= [ 1 * 1 * (0.16)3 ] + [ 3 * 0.84 * (0.16)2 ]

= 0.004 + 0.065

= 0.069

Therefore, required probability is 0.069