Question

David Barnes and his fiancée Valerie Shah are visiting Hawaii. There are 14 guests registered for...

David Barnes and his fiancée Valerie Shah are visiting Hawaii. There are 14 guests registered for orientation. It is announced that 6 randomly selected registered guests will receive a free lesson of the Tahitian dance.

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

Probability:_______

b. What is the probability that neither of them gets picked for the Tahitian dance lesson? (Round your answer to 4 decimal places.)

Probability:_______

Homework Answers

Answer #1

Number of ways in which r items can be selected from n, nCr = n!/(r! x (n-r)!)

Total number of ways in which 6 guests can be selected from 14 = 14C6

= 3,003

a) P(both David and Valerie get picked for the Tahitian dance lesson) = Number of ways in which David, Valerie and 4 others from remaining 12 can be selected / Total number of selections possible

= 1 x 1 x 12C4 / 14C6

= 495/3,003

= 0.1648

b) P(neither of them gets picked for the Tahitian dance lesson) = Number of ways in which 6 people can be selected from the 12 other people / Total number of selections possible

= 12C6/14C6

= 924/3,003

= 0.3077

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