A Collection of Probability Questions

1. Determine the probability of each of the following situations

a) A red card is drawn from a standard deck

52

26

There are 52 cards in a deck. Half of them are red (26), so…

2

1

b) 2 even numbers are rolled on two consecutive rolls of a die.

2

1

Rolling an even number (3 even numbers, 6 numbers total), is 3/6 = ½

Rolling 2 even numbers in a row, would be the product.

2

1

4

1

c) At least one three turns up when three dice are rolled.

6

5

Each roll has a 1/6 chance of occuring

At least 1 three could be 1, or 2, or 3 (three cases)

The indirect method will be faster

The compliment of “at least 1 three”, is no threes

6

5

6

5

216

125

216

91

216

1251

d) Dealing a hand from a standard deck. Three of one suit and two of another.

3

134

13 cards per suit, you need 3 of them, so 13C3

There are 4 choices for suits, so 4 X 13C3

13 cards per suit, you need 2 of them, so 13C2

There are 3 choices for suits, so 3 X 13C2

2

133

5

52

e) Two face cards are drawn in a row (without replacement) from a standard deck given that the first card drawn is a king.

First card drawn is a king.

The next draw is a face card (there are 11 face cards left, and 51 cards left)

663

11

2652

44

51

11

52

4

f) A committee of six people randomly chosen from seven males and eight females is either all male or all female.

All male, 7C6

All female, 8C6

All committees, 15C6

6

15

6

8

6

7

g) In a six person sprint, Jesse finishes first, Marnie second, and Raul last.

Jesse first:1

Marnie second: 1

Raul last: 1

3 spots left for 3 people (3!)

6! Total ways

!6

!3

• See the sheet outline posted