You can
put this solution on YOUR website!you have 12 burritos to pick from.
5 are hot.
seven are not.
you pick 3 at random.
probability that at least 2 have hot peppers would be:
???
the probability of getting exactly 3 hot ones would be:
(5*4*3)/(12*11*10) = 60/1320
the probability of getting exactly 2 hot ones would be:
(5*4*7)/(12*11*10) * 3 = 120/1320 * 3 = 420/1320
Any other possible picks would be invalid because they would involve less than 2 burritos.
the probability of getting exactly 3 hot burritos can happen in 1 way only.
HHH
the probability of getting exactly 2 hot burritos can happen in 3 ways only.
HHC
HCH
CHH
that's why we multiplied by 3 to get 420/1320.
since the probability of exactly 3 or exactly 2 is additive, then we have 60/1320 + 420/1320 = 480/1320 which is equal to .36363636364 which, if you round to 3 decimal places, equals .364.
If we did this correctly, then the total probability should be 1.
p(0H) = 1 * (7*6*5)/1320 = 210/1320 = 210/1320
p(1H) = 3 * (5*7*6)/1320 = 210/1320 = 630/1320
p(2H) = 3 * (5*4*7)/1320 = 140/1320 = 420/1320
p(3H0 = 1 * (5*4*3)/1320 = 60/1320 = 60/1320
total probability is (210+630+420+60) / 1320 = 1320 / 1320 = 1
total probability should be 1 and it is so your mother is right.
only problem I can find is in the rounding.
Answer should be .364 and not .36.
Other than that I think the answer that your mother gave you is correct.
