Exam 10: Probability and Counting Techniques

How many different ways can 3 winning tickets be selected from 50 tickets, without replacement, if Each ticket wins a different prize? (Note: the tickets can be selected in any order.)

In a class of 20 students, there are 12 girls and 8 boys. Three students are selected to be teacher's assistants. Find the probability that the group consists of one girl and two boys.

Suppose this diagram illustrates the number of women and Democrats in the U.S. Senate. We can see that 18 of the senators are women and 42 of the senators are democrats. since there are 100 senators this means that the probability of a senator being a woman is 0.18 and the probability of a senator being a democrat is 0.42. If we try to use the addition rule, we'd conclude that the probability of a senator being a woman or a Democrat is 0.18 + 0.42 = 0.6. Explain why using our addition rule doesn't work here.

Evaluate .

Three coins are tossed. Find the probability that two or more coins land heads up.

If the probability of event B is given by , then find the odds in favor of and against B.

A baseball pitcher has only three pitches: a fast ball, a curve ball, and a knuckle ball. As the pitcher Warms up before an inning, she wants to throw a fast ball 2 times, a curve ball 6 times, and a Knuckle ball 4 times. How many different ways can this be done.

If the odds against a horse winning a race are 7:3, what is the probability that the horse will win the Race?

Two dice are rolled. Find the probability of getting a sum of 6.

A babysitter has four lollipops of different colors. In how many ways can she give onelollipop to each of the four children she is watching?

There are 75 balls in a bingo hopper. The ones numbered 1-15 are labeled with B, the ones from 16 -30 with I, from 31-45 N, from 46-60 G, and from 61-75 O. Find the probability of drawing an odd Number.

Three cards are numbered 2, 3, 4 and placed into a bag. Another bag is set up the same way, then one card is drawn from each bag and the numbers are added. Find all possible totals, and construct a probability distribution for the experiment.

Suppose this diagram illustrates the number of women and Democrats in the U.S. Senate. We can see that 22 of the senators are women and 40 of the senators are democrats. since there are 100 senators this means that the probability of a senator being a woman is 0.22 and the probability of a senator being a democrat is 0.4. If we try to use the addition rule, we'd conclude that the probability of a senator being a woman or a Democrat is 0.22 + 0.4 = 0.62. How can we be sure that this is incorrect?

Suppose that the probability of an female living in a particular country developing some type of Cancer at some point in her life is about 1/7. Find the odds in favor of and against an American Woman developing cancer.

Evaluate .

Of all the students at a particular university, 54% prefer to have their first class at 8:00 am. If 9 Students are waiting to be advised, what is the probability that exactly 2 of them prefer to have their First class at 8:00 am? Round to four decimal places, if necessary.

Three coins are tossed. Find the probability that all the coins land heads up

There are 75 balls in a bingo hopper. The ones numbered 1-15 are labeled with B, the ones from 16 -30 with I, from 31-45 N, from 46-60 G, and from 61-75 O. Find the probability of drawing I10.

The difference between percent chance and probability is that we write probability as a number between and .

The odds in favor of an event are 10:1. Find the probability that the event will occur.