Question

A bag contains 9 red, 8 orange, and 6 green jellybeans. What is the probability of reaching into the bag and randomly withdrawing 17 jellybeans such that the number of red ones is 7, the number of orange ones is 7, and the number of green ones is 33? Express your answer as a fraction or a decimal number rounded to four decimal places.

Answer 1

Number of red jelly beans = 9

Number of orange jelly beans = 8

Number of green jelly beans = 6

Total number of jelly beans = 23

Total events = Number of ways of withdrawing 17 jelly beans from 23 jelly beans = = 100947

Red Events = Number of ways of withdrawing 7 red jelly beans from 9 red jelly beans = = 36

Orange Events = Number of ways of withdrawing 7 orange jelly beans from 8 orange jelly beans = =8

Green events = Number of ways of withdrawing 3 green jelly beans from 6 green jelly beans = =20

Favorable events = Red events x orange events x Green events = 36 x 8 x 20=5760

Probability of reaching into the bag and randomly withdrawing 17 jellybeans such that the number of red ones is 7, the number of orange ones is 7, and the number of green ones is 3 =

Favorable events / Total events = 5760 / 100947 = 0.0571

Probability of reaching into the bag and randomly withdrawing 17 jellybeans such that the number of red ones is 7, the number of orange ones is 7, and the number of green ones is 3 = 0.0571