Question

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:_______

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