What is the probability that in a group of five friends, at least two share the same astrological sign? Note that there are 12 astrological signs of the Zodiac.

Question

What is the probability that in a group of five friends, at least two share the same astrological sign? Note that there are 12 astrological signs of the Zodiac.

 

Please show how to find solution. The answer is .0618056 but how do you get there?

Answer 1

The probability that in a group of five friends, at least two share the same astrological sign

= 1 - the probability that all five friends have different astrological signs

= 1 - (12/12)(11/12)(10/12)(9/12)(8/12)

= 1 - ₁₂P₅/12⁵

= 1 - 0.381944

= 0.618056

 

Explanation

If all five friends have different signs, then

The first person has 12 choices for a sign, so the probability is (12/12)

The second person has 11 choices for a sign, so the probability is (11/12)

and this continues until the last person of the group

 

The probability that all five friends have different astrological signs is just the product of

(12/12)(11/12 ... (8/12)

 

I believe your posted answer, 0.0618056, is a typo.