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?
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)!) * px * (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
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