Question

David Barnes and his fiancée Valerie Shah are visiting Hawaii. There are 17 guests registered for orientation. It is announced that 10 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.)

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

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 10 guests can be selected from 17 = 17C10

= 19,448

a) P(both David and Valerie get picked for the Tahitian dance lesson) = Number of ways in which David, Valerie and 8 others from remaining 15 can be selected / Total number of selections possible

= 1 x 1 x 15C8 / 17C10

= 6,435/19,448

= 0.3309

b) P(neither of them gets picked for the Tahitian dance lesson) = Number of ways in which 10 people can be selected from the 15 other people / Total number of selections possible

= 15C10/17C10

= 3,003/19,448

= 0.1544