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

we need to multiply the chance of an event happening to get the consecutive probability. In the case were fewer than 4 need to flower we get the following possibilities:only 3 flower, only two flower, only one flowers of none flower.
probability of only 3 flower: (0.25^3)(0.75^7)=0.2%
probability of only 2 flower: (0.25^2)(0.75^8)=0.6%
probability of only 1 flower: (0.25)(0.75^9)=1.9%
probability of none flower: (0.75^10)=5.6%
Now suming these probabilities we get: P(x<4)=5.6+1.9+0.6+0.2=8.3%

Answer 2

sorry.. i think its wrong.. i got the right answer.. its a binomial problem
n = 10, p = 0.25, k = 3 or fewer

Answer 3

so the answer is 0.7759