Eight peas are generated from parents having the green/yellow pair of genes, so

Question

Eight peas are generated from parents having the green/yellow pair of genes, so there is a 0.75 probability that an individual pea will have a green pod. Find the probability that among the 8 offspring peas, at leastat least 7 havehave green pods.pods. Is it unusual to get at leastat least 7 peaspeas with greengreen podspods when 8 offspring peas are generated? Why or why not?

The probability that at leastat least 7 of the 8 offspring peas have green podspods is_________

*Please someone show me how I should plug these into the calculator. I'm lost on this and confused.

Explanation / Answer

Binomial Distribution
PMF of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
Where   
k = number of successes in trials
n = is the number of independent trials
p = probability of success on each trial
a.
P( X < 7) = P(X=6) + P(X=5) + P(X=4) + P(X=3) + P(X=2) + P(X=1) + P(X=0)
= ( 8 6 ) * 0.75^6 * ( 1- 0.75 ) ^2 + ( 8 5 ) * 0.75^5 * ( 1- 0.75 ) ^3 + ( 8 4 ) * 0.75^4 * ( 1- 0.75 ) ^4 + ( 8 3 ) * 0.75^3 * ( 1- 0.75 ) ^5 + ( 8 2 ) * 0.75^2 * ( 1- 0.75 ) ^6 + ( 8 1 ) * 0.75^1 * ( 1- 0.75 ) ^7 + ( 8 0 ) * 0.75^0 * ( 1- 0.75 ) ^8   
= 0.6329
P( X > = 7 ) = 1 - P( X < 7) = 0.3671

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