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 blue gem and then another blue gem without replacement are dependent. then, identify the probability.

Answer 1

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 :)

Answer 2

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.

Use the product rule to count the whole probability: 1/5·1/7=1/35.