Word Problems: Probability and Combinations

Question 1

What is the basic formula for Probability?

Answer 1

P = (Favorable Outcomes) / (Total Possible Outcomes).

Question 2

What is the probability of an event that is Guaranteed to happen?

Answer 2

1 (or 100%).

Question 3

What is the probability of an Impossible event?

Answer 3

0.

Question 4

What is the formula for Combinations (where order does not matter)?

Answer 4

C(n, r) = n! / [r!(n-r)!].

Question 5

What is the formula for Permutations (where order does matter)?

Answer 5

P(n, r) = n! / (n-r)!.

Question 6

What is 5! (5 factorial)?

Answer 6

120 (5 * 4 * 3 * 2 * 1).

Question 7

A bag has 3 red marbles and 7 blue marbles. Probability of picking a red one?

Answer 7

3/10 or 0.3.

Question 8

Rolling a standard 6-sided die, what is the probability of rolling an even number?

Answer 8

1/2 (3 out of 6).

Question 9

How many ways can you choose a committee of 3 people from a group of 5?

Answer 9

10 (C(5,3) = (543)/(321)).

Question 10

How many ways can you arrange the letters in the word “CAT”?

Answer 10

6 (3! = 3 * 2 * 1).

Question 11

If the probability of rain is 0.4, what is the probability it won’t rain?

Answer 11

0.6 (1 - 0.4).

Question 12

You flip a coin twice. What is the probability of getting Heads both times?

Answer 12

1/4 (1/2 * 1/2).

Question 13

A card is drawn from a standard 52-card deck. Probability it is a Heart?

Answer 13

1/4 (13 out of 52).

Question 14

Probability of drawing an Ace from a 52-card deck?

Answer 14

1/13 (4 out of 52).

Question 15

If you have 3 shirts and 4 pairs of pants, how many different outfits can you make?

Answer 15

12 (3 * 4).

Question 16

Probability of rolling a sum of 7 with two dice?

Answer 16

1/6 (6 outcomes out of 36).

Question 17

How many 3-digit codes can be made if numbers can repeat (0-9)?

Answer 17

1,000 (10^3).

Question 18

How many 3-digit codes can be made if numbers cannot repeat?

Answer 18

720 (10 * 9 * 8).

Question 19

Two independent events: P(A) = 0.5, P(B) = 0.2. What is P(A and B)?

Answer 19

0.1 (0.5 * 0.2).

Question 20

P(A) = 0.3, P(B) = 0.4. If they are mutually exclusive, what is P(A or B)?

Answer 20

0.7 (0.3 + 0.4).

Question 21

Choosing 2 toppings from 10 options. How many combinations?

Answer 21

45 (10 * 9 / 2).

Question 22

Probability of picking a “J” from the word “JULY”?

Answer 22

1/4.

Question 23

A box has 4 white and 6 black balls. You pick one, keep it, then pick another. Probability both are white?

Answer 23

2/15 (4/10 * 3/9).

Question 24

In card #23, if you replace the first ball, what is the probability both are white?

Answer 24

4/25 (4/10 * 4/10).

Question 25

How many ways can 4 people sit in a row of 4 chairs?

Answer 25

24 (4!).

Question 26

A spinner has 8 equal sections (1-8). Probability of landing on a number > 5?

Answer 26

3/8 (6, 7, 8).

Question 27

Probability of rolling a 1 or a 6 on a single die?

Answer 27

1/3 (1/6 + 1/6).

Question 28

How many ways can a President and VP be chosen from 10 people?

Answer 28

90 (10 * 9, order matters).

Question 29

Probability of picking a Red card or a King from a 52-card deck?

Answer 29

7/13 (26/52 + 4/52 - 2/52).

Question 30

What is 0!?

Answer 30

1.

Question 31

A coin is flipped 3 times. How many total possible outcomes?

Answer 31

8 (2^3).

Question 32

In card #31, probability of getting exactly 3 tails?

Answer 32

1/8.

Question 33

How many ways to choose 4 cards from a deck of 52?

Answer 33

C(52, 4).

Question 34

Probability of rolling a prime number on a die (1-6)?

Answer 34

1/2 (2, 3, 5).

Question 35

A license plate has 3 letters followed by 3 numbers. Total possibilities?

Answer 35

26^3 * 10^3.

Question 36

Probability of NOT drawing a Diamond from a deck?

Answer 36

3/4.

Question 37

You have 5 different books. How many ways to stack them?

Answer 37

120 (5!).

Question 38

Probability of drawing two red cards in a row with replacement?

Answer 38

1/4.

Question 39

Probability of drawing two red cards in a row without replacement?

Answer 39

25/102 (26/52 * 25/51).

Question 40

If you must pick 1 appetizer from 5, 1 entree from 10, and 1 dessert from 4, how many meal combos?

Answer 40

200 (5 * 10 * 4).