Extending the Concepts and Skills 569 Roulette A success s i

Extending the Concepts and Skills 5.69 Roulette. A success, s, in Bernoulli trials is often derived from a collection of outcomes. For example, an American roulette wheel consists of 38 numbers, of which 18 are red, 18 are black, and 2 are green. When the roulette wheel is spun, the ball is equally likely to land on any one of the 38 numbers. If you are interested in which number the ball lands on, each play at the roulette wheel has 38 possible outcomes. Suppose, however, that you are betting on red. Then you are interested only in whether the ball lands on a red number, From this point of view, each play at the wheel has only two possible outcomes either the ball lands on a red number or it doesn?t. Hence, successive bets on red constitute a sequence of Bernoulli trails with success probability 18/38 . In four plays at a roulette wheel, what is the probability that the ball lands on red a. exactly twice? b. at least once?

Solution

a)from bernouli\'s distribution

exactly 2 times

let p=success

since there are only 4 trails

then p² *(1-p)² =(9/19)²*(10/19)² =0.0621

b)for atleast once we take complement of nothing at all

1-(1-p)⁴=1-(10/19)⁴=1-0.0503=0.923266