David Barnes and his fiancée Valerie Shah are visiting Hawaii. At the Hawaiian C

Question

David Barnes and his fiancée Valerie Shah are visiting Hawaii. At the Hawaiian Cultural Center in Honolulu, they are told that 2 out of a group of 12 people will be randomly picked for a free lesson of a Tahitian dance.

What is the probability that both David and Valerie get picked for the Tahitian dance lesson? (Round your answer to 4 decimal places.)

b)

What is the probability that Valerie gets picked before David for the Tahitian dance lesson? (Round your answer to 4 decimal places.)

David Barnes and his fiancée Valerie Shah are visiting Hawaii. At the Hawaiian Cultural Center in Honolulu, they are told that 2 out of a group of 12 people will be randomly picked for a free lesson of a Tahitian dance.

Explanation / Answer

Total number of ways of selecting 2 persons out of 12 is C(12,2) = 66

(a)

Number of ways of selecting  both David and Valerie is 1 so the probability that both David and Valerie get picked for the Tahitian dance lesson is

p = 1/ 66 = 0.0152

(b)

The probability of selecting first Valerieout 12 is 1/12 so

P(First Valerie) = 1/12

and after that selecting David is

P(Second David|First Valerie) = 1/11

So the probability that Valerie gets picked before David for the Tahitian dance lesson is

P(Second David and First Valerie)=P(Second David|First Valerie)P(First Valerie) = (1/11)*(1/12) = 0.0076

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