Problem description:
There is a batch of seeds, and the probability of germination of each seed is two-thirds. Five seeds were planted. Find out the probability that only four seeds germinate, at least four seeds germinate and only three seeds do not germinate. Process, text, don't download. thank you
Analysis:
Whether the seeds are different or not, they are all the same.
First, the seeds are randomly arranged into numbers 1, 2, 3, 4 and 5.
The probability of any seed germination is p = 2/3, and the probability of non-germination is (1-p) = 1/3.
The probability of germination of all seeds
Px = p 1*p2*p3*p4*p5
For those before n (1)
px = p^n*( 1-p)^(5-n)=(2/3)^n *( 1/3)^(5-n)
Secondly, for all the seeds with exactly n seeds to germinate, we should consider the combination number C5(N) = 5 when n seeds are randomly selected in front of 5 seeds! /(N！ (5-N)！ )
p = c5(n)*(2/3)^n*( 1/3)^(5-n)
Just four buds: P4 = 5 * (2/3) 4 * (1/3) = 80/243.
At least four seeds germinated: P4' = P4+P5 =112/243.
Just three did not germinate, which is equivalent to just two germinated: P2 =10 * (2/3) 2 * (1/3) 3 = 40/243.