6. A child playing a carnival game successfully knocks down three milk bottles.

Question

6. A child playing a carnival game successfully knocks down three milk bottles. As a result, he gets to randomly select one prize from each of four dark colored bags. The prizes in the bags are indicated in the table below with some bags containing more prizes than others. tems Contained in Each Bag a. Find the total number of all Bag 1 Ball Bag 2 Bear Bracelet Bag 3 Pin Wheel Paddle Ball Bag 4 Toy Dog possible combinations of prizes that can be selected from the four bags Water Gun Candy Jump Rope b. What is the probability of the final prize selection containing both a ball and a bracelet? Show workl

Explanation / Answer

a. Bag 1 and 2 have 3 options each, bag 3 has 2 options and bag 4 has 1 option.

Number of ways to choose from each bag: 3C1 , 3C1 , 2C1 and 1C1 respectively for each bag in order.

Total number of ways in which prize can be decided = 3C1 * 3C1 * 2C1 * 1C1 = 18

b. Number of ways in which both ball and bracelet included = 1 * 1 * 2C1 * 1C1 [As it is known that ball needs to be picked from 1st bag and bracelet from 2nd, number of ways of picking these 2 is 1*1 = 1 ]

= 2

Probability = 2 / 18 = 1/9 = 0.1111

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