Question

Consider a collection of envelopes consisting of 3 red envelopes, 2 blue envelopes, 2 green envelopes, and 3 yellow envelopes. If three envelopes are selected at random, without replacement, determine the probability that they are all red envelopes.a) The probability that the first envelope is red is 3/10b) the probability the 2nd is red is 2/9c) the probability the third is red is 1/8d) multiply all together = 1/120

Answer 1

1/120

Explanation:

Firstly, we need to get the total number of envelopes, that equals the addition of the numbers of all envelope types = 3 + 3 + 2 + 2 = 10.

Now we know there are 3 red envelopes.

The probability of selecting a red envelope is

P(R1) = 3/10

The probability of selecting a second red envelope is P(R2) = 2/9 , why? We have removed one red envelope before and we now removed another. This means we have removed one red envelope and also decreased the total number of envelopes by 1 too. Hence, we have that probability.

Now for the third selection, we have removed two red envelopes and as such also decreased the total number of envelopes by 2. This makes the probability be P(R3) = 1/8

The total probability is calculated as ;

P(R1) × P(R2) x P(R3) = 3/10 × 2/9 × 1/8 = 1/120