Question

a bag contains 6 cherry, 4 orange, and 1 lemon candies. you reach in and take 3 pieces of candy at random. find the probability of taking all cherry candies

a. 0.3636
b. 0.7272
c. 0.1212
d. 0.0902

Explanation:

Step1: Calculate total number of candies

Total candies = \(6 + 4+1=11\)

Step2: Use combination formula \(C(n,r)=\frac{n!}{r!(n - r)!}\)

Number of ways to choose 3 candies from 11: \(C(11,3)=\frac{11!}{3!(11 - 3)!}=\frac{11\times10\times9}{3\times2\times1}=165\)
Number of ways to choose 3 cherry candies from 6: \(C(6,3)=\frac{6!}{3!(6 - 3)!}=\frac{6\times5\times4}{3\times2\times1}=20\)

Step3: Calculate probability

Probability \(P=\frac{C(6,3)}{C(11,3)}=\frac{20}{165}\approx0.1212\)

Answer:

C. 0.1212