Question

A certain cross between pea plants produces progeny in the ratio: 4 yellow and 2 green, if 10 progenies are chosen random, find proability;

a. Those 10 chosen are yellow?

b Exactly 6 out of 10 chosen are green?

c. What is the probability that 5 out of the 10 chosen are of the same color? Could be (5 green) or (5 yellow).

Answer 1

a) here for binomial distribuion probability of yellow =4/6 =2/3 and n=10

P(Those 10 chosen are yellow) =(2/3)¹⁰ =0.0173

b)

for binomial distribuion probability of green =2/6 =1/3 and n=10

P(Exactly 6 out of 10 chosen are green)= =0.0569

a) here for binomial distribution probability of yellow = 4/6 = 2/3 and n = 10 P(Those 10 chosen are yellow) = (2/3)^10 = 0.0173 b) for binomial distribution probability of green = 2/6 = 1/3 and n = 10 P(Exactly 6 out of 10 chosen are green) = (10 6)(1/3)^6 (2/3)^4 = 0.0569 c) probability that 5 out of the 10 chosen are of the same color = P(5 of yellow color and 5 green) = (10 5)(1/3)^5 (2/3)65 = 0.1366

c)

probability that 5 out of the 10 chosen are of the same color=P(5 of yellow color and 5 green)

= $\binom{10}{5}(1/3)^{5}(2/3)^{5}$ =0.1366