Question

According to genetic theory, every plant of a particular species has a 25% chance of being red-flowering, independently of all other plants. Among 10 plants of this species, what is the chance that fewer than 4 are red-flowering?

Answer 1

I'll try to do it and I'll prefer binomial distribution. here p=25%= 1/4 =chance of being red flowering. and q= 1-p = 1- 1/4 = 3/4. Here no of flowers is 10 so n=10. so binomial distribution is given by P(X=x) = nCx* p^x * q^n-x
here fewer than 4 should be less flowering so
P( less than 4 red flowering) = P(X=0) + P(X=1) + P(X=2) + P(X=3)
=10C0 * (1/4)^0 * (3/4)^10 + 10C1 * (1/4)^1 * (3/4)^9 + 10C2 * (1/4)^2 * (3/4)^8 + 10C3 * (1/4)^3 * (3/4)^7
=0.775
I got this answer. Hope it'll help.