Question

There are 32 chocolates in a box, all identically shaped. There 11 are filled with nuts, 13 with caramel, and 8 are solid chocolate. You randomly select one piece, eat it, and then select a second piece.

Find the following probabilities. Enter your answer in decimal notation, rounded to the nearest thousandth.

(a) The probability of selecting 2 solid chocolates in a row

(b) If the first was a solid chocolate, the probability that the second chocolate will be filled with caramel

(c) The probability of selecting a solid chocolate and a chocolate filled with caramel

Answer 1

(a)

Probability of selecting 2 solid chocolates in a row = Probability of selecting first solid chocolates (8 out of 32) * Probability of selecting second solid chocolates (7 out of 31)

= (8/32) * (7/31)

= 0.056

(b)

If the first was a solid chocolate, the probability that the second chocolate will be filled with caramel

= probability to pick caramel (13) out of remaining 31 chocolates

= 13/31

= 0.419

(c)

probability of selecting a solid chocolate and a chocolate filled with caramel =

Probability of selecting first solid chocolates (8 out of 32) * Probability of selecting second caramel chocolates (13 out of 31) + Probability of selecting first caramel chocolates (13 out of 32) * Probability of selecting second solid chocolates (8 out of 31)

= (8/32) * (13/31) + (13/32) * (8/31)

= (2 * 8 * 13) / (32 * 31)

= 0.210