Consider a collection of envelopes consisting of 1 red envelope, 3 blue envelopes, 2 green envelopes, and 3 yellow envelopes if 3 envelopes are selected at random, without replacement determine the probability that at least one envelope is a yellow envelope

the probability that at least one envelope is a yellow envelope is 16/21

Step-by-step explanation:

The probability that at least one envelope is a yellow envelope is P(Y);

P(Y) = 1 - P(Y)'

P(Y)' is the probability that no envelope is a yellow envelope.

Given;

red envelope = 1

blue envelopes = 3

green envelopes = 2

yellow envelopes = 3

Total = 9

Number of non-yellow envelope = 9 -3 = 6

(6 envelope are not yellow)

P(Y)' = P1 × P2 × P3

Since there is no replacement;

P(Y)' = 6/9 × 5/8 × 4/7

P(Y)' = 5/21

From equation 1;

P(Y) = 1 - 5/21

P(Y) = 16/21

the probability that at least one envelope is a yellow envelope is 16/21.