Consider a collection of envelopes consisting of 2 red envelopes, 2 blue envelopes, 2 green envelopes, and 3 yellow envelopes

Question

9 months ago

12

. If three envelopes are selected at random, without replacement, determine the probability that they are all yellow envelopes.

1 answer:

77julia77 [94] · Answer 1 · 2024-04-03T13:47:42+03:00

The probability that all three randomly selected envelopes are yellow without replacement is 1/84.

<h3>What is a combination?</h3>

It is an arrangement of a set of numbers from a total set where the order of the set is not relevant.

We have,

2 red envelopes

2 blue envelopes

2 green envelopes

3 yellow envelopes.

Total number of envelopes = 9

The probability that all three randomly selected envelopes are yellow without replacement.

= $\frac{^3C_1}{^9C_1} \frac{^2C_1}{^8C_1} \frac{^1C_1}{^7C_1}$

= (3/9) x (2/8) x (1/7)

= (3x2x1)/(9x8x7)

= 1/84

Thus,

The probability that all three randomly selected envelopes are yellow without replacement is 1/84.

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Consider a collection of envelopes consisting of 2 red envelopes​, 2 blue envelopes​, 2 green envelopes​, and 3 yellow envelopes