Q: Tina has two bags: Bag A contains 5 red and 3 blue counters, and Bag B contains 4 red and 5 blue counters. What is the probability that Tina picks a red counter from Bag A and a blue counter from Bag B?

$$\frac{5}{8} \times \frac{5}{9}$$

Q: Rachel has two bags. The first bag has 4 red and 6 green balls. The second bag has 3 red and 5 green balls. What is the probability that Rachel picks two green balls?

$$\frac{6}{10} \times \frac{5}{8}$$

Q: Jo is going to play one tennis match and one squash match. The probability she wins the tennis match is $$\frac{4}{7}$$ and the probability she wins the squash match is $$\frac{5}{10}. $$What is the probability that Jo wins both matches?

$$\frac{4}{7} \times \frac{5}{10}$$

Q: Paul wears either a black tie or a red tie to work. The probability he wears a black tie on any day is $$\frac{5}{9}. $$What is the probability that Paul wears a black tie on Monday and a red tie on Tuesday?

$$\frac{5}{9} \times \frac{4}{9}$$

Q: Felicity is going to play one game of chess and one game of draughts. The probability she wins chess is $$0.8$$ and draughts is $$0.6. $$What is the probability that Felicity wins exactly one of these games?

$$(0.8 \times 0.4) + (0.2 \times 0.6)$$

Q: Mimi has two bags. The first bag has 3 red and 7 green balls. The second bag has 4 red and 5 green balls. What is the probability that Mimi takes two green balls?

$$\frac{7}{10} \times \frac{5}{9}$$

Q: Lola plays two games. The probability she wins any game is $$0.6$$ and draws any game is $$0.1. $$What is the probability that Lola wins exactly one game?

$$(0.6 \times 0.3) + (0.4 \times 0.6)$$

Q: A bag contains 4 white and 6 black balls. Two balls are drawn at random, one after the other, with replacement. What is the probability both balls are black?

$$\frac{6}{10} \times \frac{6}{10}$$

Q: A bag contains 2 red and 8 blue balls. Two balls are drawn one after the other without replacement. What is the probability both balls are red?

$$\frac{2}{10} \times \frac{1}{9}$$

Question 1

Tina has two bags: Bag A contains 5 red and 3 blue counters, and Bag B contains 4 red and 5 blue counters. What is the probability that Tina picks a red counter from Bag A and a blue counter from Bag B?

Accepted Answer

$$\frac{5}{8} 	imes \frac{5}{9}$$

Question 2

Hannah plays one game of chess and one game of backgammon. The probability she wins chess is $$0.6$$ and wins backgammon is $$0.7. $$What is the probability she wins both games?

Accepted Answer

$$0.6 	imes 0.7$$

Question 3

Rachel has two bags. The first bag has 4 red and 6 green balls. The second bag has 3 red and 5 green balls. What is the probability that Rachel picks two green balls?

Accepted Answer

$$\frac{6}{10} 	imes \frac{5}{8}$$

Question 4

Jo is going to play one tennis match and one squash match. The probability she wins the tennis match is $$\frac{4}{7}$$ and the probability she wins the squash match is $$\frac{5}{10}. $$What is the probability that Jo wins both matches?

Accepted Answer

$$\frac{4}{7} 	imes \frac{5}{10}$$

Question 5

Paul wears either a black tie or a red tie to work. The probability he wears a black tie on any day is $$\frac{5}{9}. $$What is the probability that Paul wears a black tie on Monday and a red tie on Tuesday?

Accepted Answer

$$\frac{5}{9} 	imes \frac{4}{9}$$

Question 6

Jon plays two games. The probability Jon wins any game is $$0.5$$, and the probability he draws any game is $$0.3. $$What is the probability Jon wins both games?

Accepted Answer

$$0.5 	imes 0.5$$

Question 7

Bradley gets the bus on Saturday and Sunday. The probability that the bus is late on any day is $$0.2. $$What is the probability that the bus is late on at least one of these days?

Accepted Answer

$$1 - (0.8 	imes 0.8)$$

Question 8

Felicity is going to play one game of chess and one game of draughts. The probability she wins chess is $$0.8$$ and draughts is $$0.6. $$What is the probability that Felicity wins exactly one of these games?

Accepted Answer

$$(0.8 	imes 0.4) + (0.2 	imes 0.6)$$

Question 9

Mimi has two bags. The first bag has 3 red and 7 green balls. The second bag has 4 red and 5 green balls. What is the probability that Mimi takes two green balls?

Accepted Answer

$$\frac{7}{10} 	imes \frac{5}{9}$$

Question 10

Lola plays two games. The probability she wins any game is $$0.6$$ and draws any game is $$0.1. $$What is the probability that Lola wins exactly one game?

Accepted Answer

$$(0.6 	imes 0.3) + (0.4 	imes 0.6)$$

Question 11

Suppose you flip a fair coin twice. What is the probability of getting exactly one head?

Accepted Answer

$$2 	imes (0.5 	imes 0.5)$$

Question 12

A student randomly selects a marble from a bag containing 2 blue, 3 red, and 5 green marbles. What is the probability the student selects a red marble?

Accepted Answer

$$\frac{3}{10}$$

Question 13

If the probability of rain on Monday is $$0.3$$ and on Tuesday is $$0.4$$, what is the probability it rains on both days?

Accepted Answer

$$0.3 	imes 0.4$$

Question 14

A bag contains 4 white and 6 black balls. Two balls are drawn at random, one after the other, with replacement. What is the probability both balls are black?

Accepted Answer

$$\frac{6}{10} 	imes \frac{6}{10}$$

Question 15

A game has three possible outcomes: win, draw, or lose. The probability of a win is $$0.5$$, a draw is $$0.3$$, and a loss is $$0.2. $$What is the probability of not losing in two consecutive games?

Accepted Answer

$$(0.5 + 0.3)^2$

Question 16

A student rolls a fair six-sided die twice. What is the probability that both rolls result in an even number?

Accepted Answer

$$\left(\frac{3}{6}\$$right)^2$$

Question 17

If the probability of an event A is $$0.7$$ and event B is $$0.5$$, and the events are independent, what is the probability that at least one of the events occurs?

Accepted Answer

$$1 - (1 - 0.7)(1 - 0.5)$$

Question 18

A bag contains 2 red and 8 blue balls. Two balls are drawn one after the other without replacement. What is the probability both balls are red?

Accepted Answer

$$\frac{2}{10} 	imes \frac{1}{9}$$

Question 19

A fair coin is tossed three times. What is the probability of getting exactly two heads?

Accepted Answer

$$3 	imes (0.5)^2$ 	imes 0.5$$

Question 20

A student answers two multiple-choice questions, each with 4 options and only one correct answer. What is the probability the student guesses both answers correctly?

Accepted Answer

$$\frac{1}{4} 	imes \frac{1}{4}$$

Probability Trees and Compound Probability – Liberal Arts Math Study Guide

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