Compound events are combination of two or more simple events. Rolling a dice is a simple event but rolling a dice and choosing a card simultaneously is a compound event.To find the sample space and number of favorable events, organized lists, tree diagrams or tables can be used.

$P(E)$ = $\frac{n(E)}{n(S)}$

Example 1:

If a dice is rolled and a coin is tossed then what is the probability of getting a head and a 6?


Sample space, $S = \{(H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (H, 6), (T, 1), (T, 2), (T, 3), (T, 4), (T, 5), (T, 6)\}$

$n(S) = 12$

$E = \{(H, 1)\}$

$n(E) = 1$

$P(E)$ = $\frac{1}{12}$

Compound Probability Word Problems

Problem 1:

If a coin is tossed and a dice is rolled, then find the probability of getting an odd number and a tail using a tree diagram.


First we see there are two possibilities, getting a head and a tail. Then, the tree diagram shows the possibility of getting numbers 1 to 6 in each case.

Compound Probability Word Problem

Number of leaves = Total number of possible outcomes = 12

Events having an odd number and a tail = 3

Probability of getting an odd number and a tail = $\frac{3}{12}$ = $\frac{1}{4}$
Problem 2:

Raashi has two books on mathematics, A and B, and four notebooks 3, 4, 5 and 6. If she takes out one book and one notebook, find the probability that it is book B and notebook 5 using a table.


We can see the sample space using a table.

   3  4  5  6

Total number of possible events = 8

Events getting a B and a 5 together = 1

Probability of getting a B and a 5 together = $\frac{1}{5}$
Problem 3:

If a dice is rolled then what is the probability of getting a 4 or a 6?


As they are exclusive compound events the probability will be sum of their individual probabilities.

$P(4)$ = $\frac{1}{6}$

$P(6)$ = $\frac{2}{6}$

Compound probability = $P(4)$ + $P(6)$ = $\frac{3}{6}$ = $\frac{1}{2}$
Problem 4:

If three coins are tossed simultaneously then what will be the probability of getting exactly two heads?


Using a tree diagram we can see the sample of tossing three coins.

Compound Probability Word Problems

As the leaves are 8, the number of possible outcomes is 8.

Favorable outcomes = 3

Probability of getting two heads = $\frac{3}{8}$
Problem 5:

Jenny goes to a shop and likes three soft toys. One is teddy bear, other is tweety bird and third one is a Donald duck. She has to choose two toys, and the first one she has chosen as tweety bird. Find the probability of choosing Donald duck as second toy.


First toy is tweety bird. Second toy has to options to be chosen from.

Probability of choosing a Donald Duck = $\frac{1}{2}$