Question

A jewel case contains 7 white gems, 5 green gems, and 3 blue gems. Gems are selected at random. Explain why the events picking a green gem and then another green gem without replacement are dependent. Then, identify the probability.

Answer 1

Dependent event is an event that is affected by previous events. If you select the first blue gem from three, then the number of blue gems becomes 1 less and when choosing the second blue gem you have to select it from 2 blue gems. So, according to definition these events are dependent.

You have 7 white gems, 5 green gems and 3 blue gems that is 15 in total. Probability to choose first gem blue from jewel case is 3/15=1/5. Then there left 7 white gems, 5 green gems and 2 blue gems that is 14 in total. Probability to choose second gem blue from jewel case is 2/14=1/7.

Answer 2

The answer is P(green) is different when it is known that a green gem has been picked already.

P(green and green) = 2/21

Hope this helps :)