Question

In an experiment, a ball is drawn from an urn containing 7 orange balls and 12 red 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 ?

Answer 1

In the experiment, if the ball drawn is orange, three coins are tossed. Otherwise, two coins are tossed. The sample space will have 12 elements with an orange ball.

Step-by-step explanation:

To determine the number of elements in the sample space that have an orange ball, we need to consider two cases: when the ball drawn is orange and when the ball drawn is not orange (red).

If the ball drawn is orange, three coins are tossed. The sample space in this case will have 23 = 8 elements, representing all possible outcomes of the coin tosses.

If the ball drawn is not orange (red), two coins are tossed. The sample space in this case will have 22 = 4 elements, representing all possible outcomes of the coin tosses.

Therefore, the total number of elements in the sample space that have an orange ball is 8 (when the ball is orange) + 4 (when the ball is not orange) = 12.

Answer 2

84

Step-by-step explanation:

When an orange ball is picked, you toss 3 coins and there are 2^3 = 8 permutations for tossing 3 coins. Now since we have 7 orange balls there will be 7 * 8 = 56 sample spaces with orange balls.