Binomial Probability Questions

0.896

A college basketball player makes 80% of her free throws. At the end of the game, her team is losing by two points. She is fouled attempting to make a three point-shot and is awarded three free throws. Assuming free throw attempts are independent, what is the probability that she makes at least two of the free throws?

.4219

A fast food restaurant runs a promotion in which certain food items come with game pieces. According to the restaurant, 1 in 4 game pieces is a winner. If Jeff gets 4 game pieces, what is the probability that he wins exactly one prize?

.2066

A random sample of 15 people is taken from a population in which 40% favor a particular political stand. What is the probability that exactly 6 individuals in the sample favor this political stand?

0.2641

A worn out bottling machine does not properly apply caps to 5% of the bottles that it fills. If you randomly select 20 bottles from those produced by this machine, what is the approximate probability that between 2 and 6 (inclusive) caps have been improperly applied?

0.1887

A worn out bottling machine does not properly apply caps to 5% of the bottles that it fills. If you randomly select 20 bottles from those produced by this machine, what is the approximate probability that exactly 2 caps have been improperly applied?

.6723

In a certain game of chance, your chances of winning are 0.2. If you play the game five times and outcomes are independent, which of the following represents the probability that you win at least once?

.0453

In a triangle test a tester is presented with three food samples, two of which are alike, and is asked to pick out the odd one by testing. If a tester has no well-developed sense and can pick the odd one only by chance, what is the probability that in five trials he will make four or more correct decisions?

.0386

It has been estimated that about 30% of frozen chicken contain enough salmonella bacteria to cause the illness if improperly cooked. A consumer purchases 12 frozen chickens. What is the probability that the consumer will have more than 6 contaminated chickens?

.1756

It is known that 15% of the seniors in a large high school enter military service upon graduation. If a group of 20 seniors are randomly selected, what is the probability of observing at most one senior who will be entering military service?

.092

Roll one 8-sided die 10 times. Find the probability of getting exactly 3 sevens in those 10 rolls.

.9933

Suppose 80% of trees in a forest are infected with a virus. If 5 trees are selected to be tested, what is the probability that at least 2 trees are infected with the virus? Assume the independence condition is met.

.9984

The probability that a certain machine will produce a defective item is 0.20. If a random sample of 6 items is taken from the output of this machine, what is the probability that there will be fewer than 5 defectives in the sample?