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saw5 [17]
3 years ago
7

A bowl contains 7 pennies, 9 nickels, and 4 dimes. Elyse removes one coin at random from the bowl and does not replace it. She t

hen removes a second coin at random. What is the probability that both will be dimes?
Mathematics
1 answer:
Vlad [161]3 years ago
6 0

Answer:

The probability is 3/95

Step-by-step explanation:

Okay this is a probability without replacement question.

Firstly we calculate the total number of coins = 7 + 9 + 4 = 20 coins

The probability that the first coin will be a dimes = number of dimes/total number of coins = 4/20 = 1/5

Now she removes a coin without replacement, if it was a dime, total number of coins becomes 19 and the total number of dimes becomes 3; Thus the probability of the second coins being a dimes = 3/19

Thus, the probability of both coins being dimes = probability of first coin being dimes * probability of second coins being dimes

= 1/5 * 3/19 = 3/95

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Since segment AC bisects (aka cuts in half) angle A, this means the two angles CAB and CAD are the same measure. I'll refer to this later as "fact 1".

Triangles ABC and ADC have the shared segment AC between them. By the reflexive property AC = AC. Any segment is equal in length to itself. I'll call this "fact 2" later on.

Similar to fact 1, we have angle ACB = angle ACD. This is because AC bisects angle BCD into two smaller equal halves. I'll call this fact 3

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To summarize so far, we have these three facts

  1. angle CAB = angle CAD
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