Question

13 peas are generated from parents having the green and yellow pair of genes, so there is 0.75 probability that an individual will have a green pod. Find the probability that the 13 offspring peas, at least 12 have green pods. Is it unusual to get 12 peas with green pods when 13 offsprings are generated

Answer 1

@oldrin.bataku

Answer 2

how many ways can 12 of the 13 peas be selected (i.e. be green)?

Answer 3

\(\binom{13}{12}=\binom{13}1=13\) such ways. now compute the probability of any particular such way: 12 peas green is \(0.75^{12}\) while the one pea not-green is \((1-0.75)^1=0.25\) so our total probability is: $$13\cdot0.75^{12}\cdot0.25\approx 0.1029$$

Answer 4

so there's a ~10.3% chance this occurs randomly -- it's not super common, but not particularly unusual

Answer 5

oops, you said at *least* 12 pods, so there is also the chance all thirteen are green

Answer 6

To get the answer to the question it is necessary to add the probability that all 13 will be green. Therefore we need to find:
\[\large (at\ least\ 12\ green)=0.1029+(0.75)^{13}=you\ can\ calculate\]

Answer 7

in which case there's \(\binom{13}{13}=1\) such possible ways they can all turn green and the probability is \(0.75^{13}\approx 0.0238\) so our total probability is \(\text{probability 12 are green}+\text{probability all are green}\approx0.1029+0.0238=0.1267\)