Exam 8: Probability: the Mathematics of Chance

A continuous probability model has the following density curve: What is $P ( 0 \leq X \leq 1 ) ?$

We must create a license plate code that consists of two letters followed by three digits. The letters cannot repeat, but the digits may. How many such license plate codes can be formed?

Use the following information to solve the Questions: A random number generator is modeled by a uniform probability model with a density curve that has height 1/10 between 0 and 10 and height 0 everywhere else. -For this model, what is $P ( X = 5 ) ?$

A raffle ticket costs $5. First-prize and second-prize winners will be drawn at random. The probability of winning the $100 first prize is 1/40, and the probability of winning the $25 second prize is 1/20. What is the mean winnings for one play, taking into account the $5 cost of the ticket?

A game is played with a pair of tetrahedral (four-sided) dice. Each die has faces numbered 1, 2, 3, and 4. To play, roll the two dice and record the sum of the values on the down faces. What is the probability of rolling a sum of 6?

You use a random number generator that produces the digits 1 through 9 with equal probability. You draw four digits and make them into a number; for example, 0, 2, 4, 4 would be the number 0244 or just 244. What is the probability of getting a number strictly greater than 1000?

Two coins are flipped and the number that landed on heads is recorded. The outcomes in the sample space are all equally likely.

The shelf life of a battery produced by one major company is known to be Normally distributed, with a mean life of 3.5 years and a standard deviation of 0.75 years. If a sample of size 20 is repeatedly chosen at random, what is the standard deviation _x of sample means?

Suppose a trial consists of rolling two dice and reporting the sum of the numbers rolled. What are the possible outcomes? Are they equally likely?

Two fair dice are rolled and the sum rolled is recorded. Find the probability that the sum is 4.

At a certain discount store, the number of people in checkout lines varies. The probability model for the number of people in a randomly chosen line is: Number in 0 1 2 3 4 5 line Probability 0.08 0.15 0.20 0.22 0.15 0.20 What is the mean number of people in a line?

A standardized test is known to be Normally distributed with the mean of 500 and the standard deviation of 100. How large a sample would be needed if the standard deviation of sample means is 14?

Three coins are flipped simultaneously and it is recorded whether each coin lands heads or tails. List the sample space.

If you randomly select a committee of two from a group of two men and two women, what is the probability that the group is all female?

Suppose a password must consist of two letters followed by three digits. Repeated characters are allowed. A password of this type is chosen at random. What is the probability that the password does not have any vowels?

Suppose three fair coins are tossed and the number of heads that appear is recorded. What is the probability of getting exactly two heads?

Exactly one of three contestants will win a game show. The probability that Terry wins is 0.25 and the probability that Chris wins is 0.65. What is the probability that Toni, the remaining contestant wins?

A multiple-choice quiz has three possible answer choices for each question. You get four points for each correct answer, but you lose three points for each incorrect answer. No points are gained or lost if you leave the question blank. What is the mean point value of a random guess on the quiz?

We wish to make a spinner that will be numbered 1 to 4, but will have the probability of spinning a "1" be 0.5. Draw the face for such a spinner.

If two events A and B have probabilities as P(A) = 0.45 and P(B) = 0.7, then what is the smallest possible value for P(A and B)?