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The geometric and negative binomial random variables are based on a sequence of independent and identical Bernoulli trials. The probability mass function of the geometric random variable X, with probability p of a success is. Each time customers visit a resturant they are given a game card. Suppose the probability of winning a prize with the game card is 0. Let X represent the number of visits to a resturant before winning a prize with the game card. What is the probability that a customer will win a prize for the first time on the 6th visit?

What is the probability that it will take the customer 6 or more visits to win a prize for the first time? In a game of billiards, a player shoots until a miss occurs. A player misses on any given shot with a probability of 0. Let the random variable X denote the number of shots taken to obtain the first miss. What is the probability that the player will have thier first miss on the 3rd shot? What is the probability that the player will take at more than 5 shots?

The mean and variance of a geometric random variable, with probability p of a success are. Explore the Geometric Distribution by using the following applet! Click on Open Applet. Enter the value of p for p.

The kth success occurs on the y th trial, then k-1 successes and y-k failures occured during the first y-1 trials. The probability of winning a prize in a raffle is 0. Let Y denote the number of raffles a person needs to buy before they win 2 prizes. The probability that it takes exactly 12 raffles to win 2 prizes is:.

What is the probability that it takes exactly 20 raffles to win 4 prizes? Round to 4 decimal places. Refer to Example 4 once again. Let Y denote the number or raffles a person needs to buy before they win 5 prizes.

Explore the Negative Binomial Distribution by using the following applet! Enter the value of p for p and the value of k for r. Negative Binomial Distribution- Wikipedia. We want to find the probability that the player takes more than 5 shots. The sum of a geometric series is. The geometric random variable is the number of independent and identical Bernoulli trials it takes to obtain the first success. The probability mass function of the geometric random variable X, with probability p of a success is Example 1: What is E X?

What is VAR X? What is E Y? Round to 2 decimal places. What is VAR Y?