If 7 seeds are planted, the probability that exactly 3 do grow is;
P(X = 3) = 0.0002
This is a binomial probability distribution problem where;
P(X = x) = ⁿCₓ × pˣ × q⁽ⁿ ⁻ ˣ⁾
We are given;
p = 95% = 0.95
q = 1 - p
q = 1 - 0.95
q = 0.05
Thus If 7 seeds are planted, the probability that exactly 3 do grow is;
P(X = 3) = ⁷C₃ × 0.95³ × 0.05⁽⁷ ⁻ ³⁾
P(X = 3) = 35 × 0.857375 × 0.00000625
P(X = 3) = 0.000187
To four decimal places gives;
P(X = 3) = 0.0002
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