Question

In a Godiva shop, 40% of the cookies are plain truffles,

20% are black truffles, 10% are cherry cookies, and 30%

are a mix of all the others. Suppose you pick one at ran-
dom from a prepacked bag that reflects this composition.

a. What is the probability of picking a plain truffle?
b. What is the probability of picking truffle of any kind?
c. If you instead pick three cookies in a row, what is
the probability that all three are black truffles?

Answer 1

a. The probability of picking a plain truffle is 40%.

b. The probability of picking truffle of any kind is 100%.

c. The probability of picking a black truffle on the first draw is 20%. The probability of picking a black truffle on the second draw is also 20%, since the draws are independent. The probability of picking a black truffle on the third draw is also 20%. So, the probability of picking three black truffles in a row is:

0.2 * 0.2 * 0.2 = 0.008, or 0.8%.

Answer 2

a. The probability of picking a plain truffle is 40%.

b. The probability of picking a truffle of any kind can be found by adding the probabilities of picking each type of truffle:

P(truffle of any kind) = P(plain truffle) + P(black truffle) + P(cherry cookie) + P(mix)

P(truffle of any kind) = 0.4 + 0.2 + 0.1 + 0.3

P(truffle of any kind) = 1

So, the probability of picking a truffle of any kind is 100%.

c. If you pick three cookies in a row, the probability that all three are black truffles can be found by multiplying the probabilities of picking a black truffle on each pick:

P(all three are black truffles) = P(black truffle on first pick) x P(black truffle on second pick) x P(black truffle on third pick)

Since we are picking without replacement, the probability of picking a black truffle decreases with each pick.

P(black truffle on first pick) = 0.2

P(black truffle on second pick, given that the first pick was a black truffle) = 0.25 (since there are 4 black truffles left out of 15 total cookies)

P(black truffle on third pick, given that the first two picks were black truffles) = 0.33 (since there are 3 black truffles left out of 14 total cookies)

Therefore,

P(all three are black truffles) = 0.2 x 0.25 x 0.33

P(all three are black truffles) = 0.0165

So, the probability that all three cookies picked are black truffles is 0.0165 or approximately 1.65%.