Ajewel 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.

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.