Discrete Probability Distribution and Standard Deck

EXERCISES (Discrete Probability Distribution)

EXERCISES (Discrete Probability Distribution)

P X  x    n C x  p  1  p  x BINOMIAL DISTRIBUTION

n x

P X  x    n C x  p  1  p  x BINOMIAL DISTRIBUTION

n x

1. 2. 3.

The probability that a certain kind of component will survive a given shock test is ¾. Find the probability that exactly 2 of the next 4 components tested survive. The probability that a log-on to the network is successful is 0.87. Ten users attempt to log on, independently. Find the probability that between 4 and 8 log-ons are successful. The probability that a patient recovers from a rare blood disease is 0.40. If 15 people are known to have contracted this disease, what is the probability that (a) at least 10 survive, (b) from 3 to 8 survive, and (c) exactly 5 survive? NEGATIVE BINOMIAL DISTRIBUTION

1. 2. 3.

P X  x    k 1 C x1  p  1  p  x The probability that a certain kind of component will survive a given shock test is ¾. Find the probability that exactly 2 of the next 4 components tested survive. The probability that a log-on to the network is successful is 0.87. Ten users attempt to log on, independently. Find the probability that between 4 and 8 log-ons are successful. The probability that a patient recovers from a rare blood disease is 0.40. If 15 people are known to have contracted this disease, what is the probability that (a) at least 10 survive, (b) from 3 to 8 survive, and (c) exactly 5 survive? NEGATIVE BINOMIAL DISTRIBUTION

k x

P X  x    k 1 C x1  p  1  p  x k x

4.

5.

6.

An oil company conducts a geological study that indicates that an exploratory oil well should have a 20% chance of striking oil. What is the probability that the third strike comes on the seventh well drilled? It is reported that 10% of the apples from the Apple Farm are bad. If apples are randomly selected from this farm one after another, what is the probability