Answer:
0.095
Step-by-step explanation:
There are a total of 15 (6 + 5 + 4) coins, of which 5 are dimes.
The first coin that Dianna extracts has a probability of 5 dimes between 15 coins. In the case of the second coin extracted, there is a remainder, in which the probability is 4 dimes between 14 coins.
Let P be the probability that Diana grabs two dimes, then
[tex]P = \frac{5}{15}.\frac{4}{14}=\frac{20}{210}=0.095[/tex]
Another way to calculate that probability is by using combinations.
[tex]_{5}C_{2}[/tex] = get 2 dimes of 5 existing dimes
[tex]_{15}C_{2}[/tex] = get 2 dimes of 15 coins in total
[tex]P = \frac{_{5}C_{2}}{_{15}C_{2}}[/tex]
Where,
[tex]_{5}C_{2}=\frac{5!}{2!(5-2)!}=\frac{5.4.3!}{2(3)!}=\frac{5.4}{2}=\frac{20}{2}=10[/tex]
[tex]_{15}C_{2}=\frac{15!}{2!(15-2)!}=\frac{15.14.13!}{2(13)!}=\frac{15.14}{2}=\frac{210}{2}=105[/tex]
[tex]P = \frac{_{5}C_{2}}{_{15}C_{2}}=\frac{10}{105}=0.095[/tex]
The probability that Dianna grabs two dimes is 0.095
Hope this helps!
