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ki77a [65]
4 years ago
12

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.
Mathematics
1 answer:
dangina [55]4 years ago
4 0

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.

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<h3>What is an equation?</h3>

An equation is an expression that shows the relationship between two or more variables and numbers.

Given that:

a_n=1 + (-\frac{4}{9} )^n\\\\When\ n=1:a_1=1 + (-\frac{4}{9} )^1=0.5556\\\\When\ n=2:a_2=1 + (-\frac{4}{9} )^2=1.1975\\\\When\ n=3:a_3=1 + (-\frac{4}{9} )^3=0.9122\\\\When\ n=4:a_4=1 + (-\frac{4}{9} )^4=1.039\\\\When\ n=5:a_5=1 + (-\frac{4}{9} )^5=0.9827\\\\When\ n=6:a_6=1 + (-\frac{4}{9} )^6=1.0077\\\\When\ n=7:a_7=1 + (-\frac{4}{9} )^7=0.9966\\\\When\ n=8:a_8=1 + (-\frac{4}{9} )^8=1.0015\\\\When\ n=9:a_9=1 + (-\frac{4}{9} )^9=0.9993\\\\

When\ n=10:a_{10}=1 + (-\frac{4}{9} )^{10}=1.0003\\

The first ten terms of the sequence a_n=1 + (-\frac{4}{9} )^n is<em> 0.5556, 1.1975, 0.9122, 1.039, 0.9827, 1.0077, 0.9966, 1.0015, 0.9993 and 1.0003</em>

Find out more on equation at: brainly.com/question/2972832

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