You order twelve burritos to go from a Mexican restaurant fi

You order twelve burritos to go from a Mexican restaurant, five with hot peppers and seven without. However, the restaurant forgot to label them. If you pick three burritos at random, find the probability that at least two have hot peppers. (Round the answer to three decimal places.)

Solution

total burriots=12

hot peppers=5

not hot peppers=7

probability of atleast 2 hot peppers =????

probability of atleast 2 hot peppers consist of 2 parts

(1) probability of exactly 2 hot peppers and

(2) probability of exactly 3 hot peppers

so

(1) probability of exactly 2 hot peppers is

((5*4*7)/(12*11*10))*3=420/1320

(we multiplied by 3 because we can select 2 hot pepper in 3 ways)

(2) probability of exactly 3 hot peppers is

(5*4*3)/(12*11*10)=60/1320

so probability of atleast 2 hot peppers is

p(x=2)+p(x=3)

420/1320+60/1320=480/1320=0.36364=0.364(upto 3 decimal)