In an experiment a ball is drawn from an urn containing 11 o

In an experiment, a ball is drawn from an urn containing 11 orange balls and 8 blue balls. If the ball is orange, three coins are tossed. Otherwise two coins are tossed.

How many elements of the sample space will have a orange ball?

How many elements of the sample space are there altogether?

Solution

How many elements of the sample space will have a orange ball?

Whenever a orange ball is selected three coins are tossed. So the number of ways the results of 3 tosses can come will be the number of elements in the sample space with an orange ball.

3 tosses may result in

(1) 3 tails (2) 2tails 1 heads (3) 1tails 2heads (4) 3 heads

Thus the sample space containing orange ball will have 4 elements.

How many elements of the sample space are there altogether?

To find the total number of elemnts in sample space altogether we just add the elements which contain blue ball in draw instead of orange ball with the elements calculated above.

Sample space elements with blue ball

(1) 2 heads (2) 1 heads 1 tails (3) 2 tails

Thus the total number of elemnts in sample space altogether are 4+3 = 7