Probability with burritos

Question

(a) You order eighteen burritos to go from a Mexican restaurant, eight with hot peppers and ten without. However, the restaurant forgot to label them. If you pick three burritos at random, find the probability of the given event. (Round your answer to three decimal places.)

-All have hot peppers

(b) You order fifteen burritos to go from a Mexican restaurant, eight with hot peppers and seven without. However, the restaurant forgot to label them. If you pick three burritos at random, find the probability of the given event. (Round your answer to three decimal places.)

-At least two have hot peppers.

(c) You order seventeen burritos to go from a Mexican restaurant, seven with hot peppers and ten without. However, the restaurant forgot to label them. If you pick three burritos at random, find the probability of the given event. (Round your answer to three decimal places.)

-At most two have hot peppers.



Answer 1

8/18 x 7/17 x 6/16 = chance of all hot peppers in 3 draws of 18

= (8)(7)(6)/(18)(17)(16)

for at least 2 hot peppers for 3 draws out of 15

= 8/15 x 7/14 x 6/13 + 8/15 x 7/14 x 7/13 + 8/15 x 7/14 x 7/13 + 7/15 x 8/14 x 7/13

= chance of 3 hot peppers + chance of 2 hot peppers (which happens 3 ways)

for at most 2 hot peppers 3 draws out of 17, 7 hot, 10 not

1 - Pr(3 hot) = 1 - 7/17 x 6/16 x 5/15

subtract odds of all 3 hot from one.