Question

Box of chocolates According to Forrest Gump, “Life is like a box of chocolates. You never know what you’re gonna get.” Suppose a candymaker offers a special “Gump box” with 20 chocolate candies that look alike. In fact, 14 of the candies have soft centers and 6 have hard centers. Suppose you choose 3 of the candies from a Gump box at random. Find the probability that all three candies have soft centers

Short answer

The probability is $0.319\text{.}$

Step-by-step solution

Step 1:Given information

Number of chocolate candies that look same$=20$

Number of candies that have soft corner $=14$

Number of candies that have hard corner$=6$

Step 2:Calculation

The probability that all three randomly selected candies have soft centres can be calculated as:

$P\text{(All three have soft centers)}=\frac{{}^{14}C_3}{{}^{20}C_3}$

$=\frac{\frac{14!}{(14-3)!\times 3!}}{\frac{20!}{(20-3)!\times 3!}}$

$=\frac{364}{1140}$

$=0.319$

Thus, the required probability is $0.319\text{.}$