1. Probability of Multiple Events

2. Mutually Exclusive Events
Two events are mutually exclusive if the outcome of one automatically excludes the possibility of the other.
Example:
If we toss a coin, we cannot get both a heads and a tails
IF two events, A and B, are mutually exclusive, then:

3. One card is selected from a pack of cards
One card is selected from a pack of cards. What is the probability of selecting either a diamond or a black ace?
Answer:
A die is rolled. what is the probability of rolling a 5 or an even number?
Answer:

4. Independent Events
A and B are independent events if knowledge that B occurred does not change the probability that A occurs.
For two independent events A and B:
Notice that for mutually exclusive events:

5. A card is selected from a standard deck of cards and a six-sided die is thrown. Find the probability that the outcome will be a red card and a number less than three on the die.
Answer:
A red and green die are rolled. what is the probability of rolling a 5 on the red and a 6 on the green or two even numbers.
Answer:

6. Events which are NOT mutually exclusive
If we choose a card from a deck of cards and want to find the probability of choosing a queen or a red card. Two of the queens are also red. Therefore these events are not mutually exclusive.
If two events, A and B, are not mutually exclusive, then:

7. a) A and B are mutually exclusive b) A and B are independent
Suppose that P(A) = 0.5, P(B) = 0.6 and = Are A and B mutually exclusive? Are A and B independent? Find P(A or B).
Answers:
A and B are not mutually exclusive. A and B are not independent.
P(A or B) = 0.7
Events A and B are such that P(A) = 0.5 and P(A or B) = Find P(B) in the cases that:
a) A and B are mutually exclusive
b) A and B are independent
Answers:
a) 0.3
b) 0.6

8. Successive Trials
If A and B are two trials, then:
With successive trials, there are two possibilities:
1. The two trials are independent of each other.
2. The second event is dependent on the outcome of the first, or, the second event is conditional on the first.

9. For each mile that I drive, the probability that I have an accident is Each mile is independent of the others. What is the probability that I complete a journey of 100 miles safely?
Answer:
A multiple choice test contains ten questions, each of which has five possible answers. A candidate is totally ignorant of the subject of the test and answers at random. What is the probability that the candidate gets
a) none right
b) at least one right
Answers: a) b)

10. A person throws 12 darts at a dartboard
A person throws 12 darts at a dartboard. With each dart, the probability that it hits the bullseye is 0.1 and each dart is independent of the others. what is the probability that the person hits the bullseye at least once?
Answer:
A certain sort of tulip bulb is such that one in three of them will flower. If five are bought, what is the probability that at least one will flower?
Answer:

11. For two dependent events, A and B, we use the general rule:
The probability of A multiplied by the probability of B given that A has occurred.
Notice that, if two events are independent, then:

12. A tree diagram is useful in showing successive trials based on dependence.
A bag contains eight balls of which 3 are red and 5 are blue. Two balls are drawn at random without replacement. Find the probability of:
a) Two red balls
b) One red followed by one blue ball
2nd Trial
Red
Red
1st Trial
Blue
Red
Blue
Blue

13. In my dresser, I have seven black socks and eight white socks
In my dresser, I have seven black socks and eight white socks. In the morning I pick out two socks at random. What is the probability that I pick out a matching pair?
Answer:
A box of chocolates contains six hard-centered sweets and four soft-centered sweets. If I pick out two, what is the probability that one is hard-centered and the other is soft-centered?
Answer:

14. Three disks are chosen at random and without replacement from a bag containing 3 red, 8 blue and 7 white disks. Find the probability that the disk chosen will be:
a) All red
b) All blue
c) One of each color

15. Two different pupils are chosen at random from a group of 3 boys and 5 girls. Find the probability that the two chosen will be:
a) The two youngest
b) Two boys

16. Two girls Anne and Jane play tennis
Two girls Anne and Jane play tennis. The winner will be the first to gain two sets. If Anne wins a set, the probability that she will win the next is If she loses a set, the probability that she will win the next is If Anne has a probability 0.6 of winning the first set, what is the probability that she will win the match?
Answer: