Question

65% of a certain species of squash live after transplanting from pot to garden. You transplant 35 of these plants. Assume that the plants live *independently* of each other. Let X = the number of tomato plants that live

What is the probability that exactly 22 of the 35 squash plants live?

Answer 1

Solution

Given that ,

p = 65% = 0.65

1 - p = 1 - 0.65 = 0.35

n = 35

x = 22

Using binomial probability formula ,

P(X = x) = ((n! / x! (n - x)!) * p^x * (1 - p)^{n - x}

P(X = 22) = ((35! / 22! (35 - 22)!) * 0.65²² * (0.35)^{35 - 22}

= ((35! / 22! (13)!) * 0.65²² * (0.35)¹³

= 0.1337

Probability = 0.1337