Probability with Counting Techniques

Suppose there are 12 adults and 10 kids as an audience of a certain show. The host of the show will randomly select three audience members to participate in the show. What is the probability the host selects two kids and one adult.

• 6/77

• 54/77

• 27/77

You are choosing and entree, a side, and a dessert. There are 3 entrees: chicken, steak, or fish. There are 4 sides: baked potato, mashed potato, green beans, or asparagus. There are 2 desserts: chocolate cake or cheesecake. If you choose randomly, what is the probability that you choose chicken, green beans, and chocolate cake?

• 1/24

• 1/8

• 1/96

5 paintings will be hung next to each other on a wall. If the order is chosen randomly, what is the probability that the paintings are hung in alphabetical order?

• 1/60

• 1/120

• 1/240

A student wants to take art and psychology. Both classes are offered during 2nd, 6th, and 7th periods. If the student's schedule is assigned randomly, what is the probability that the student has art 2nd period and psychology 6th period?

• 1/3

• 1/2

• 1/6

A student must choose 3 electives from a list of 7: Humanities, Art History, Introduction to Theatre, Introduction to Literature, Music Appreciation, Ceramics, and Graphic Design. If the student selects randomly, what is the probability that the student does not choose Graphic Design.

• 4/7

• 3/5

• 7/10

• 3/10

There are 4 vacancies on the scholarship committee at a university. There are 7 men and 8 women available to serve. If the 4 individuals are chosen randomly, what is the probability that 2 men and 2 women are chosen?

• 6/25

• 28/65

• 2/13

There are 7 students in a class: 5 boys and 2 girls.
If the teacher picks a group of 4 at random, what is the probability that everyone in the group is a boy?

• 5/7
• 1/7
• 2/7
• 1

There are 10 students in a class: 5 boys and 5 girls.

If the teacher picks a group of 3 at random, what is the probability that everyone in the group is a girl?

• 1/12

• 1/2

• 1

• 1/5

You are dealt 5 cards from a standard deck of playing cards. What is the probability you are dealt a flush?

**A flush is all 5 cards of the same suit (order does not matter).

• 1/1287

• 1/2598960

• 1287/2598960

• 5148/2598960