Question

Dianna has 6 quarters 5 dimes and 4nickles in her purse. She reaches into her purse and randomly grabs two coins. What is the probability that Diana grabs two dimes

Answer 1

First of all, we know that Dianna has total 6+5+4=15 coins including: 6 quarters, 5 dimes and 4 nickles in her purse.
P(grabbing the first dimes):
5/15 or 1/3
P(grabbing the second dimes):
5/15 or 1/3
P(grabbing 2 dimes in a row):
1/3*1/3=1/9. As a result,the probability that Diana grabs 2 dimes is 1/9. Hope it help!

Answer 2

0.095

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

`P = (5)/(15).(4)/(14)=(20)/(210)=0.095`

Another way to calculate that probability is by using combinations.

`_(5)C_(2)` = get 2 dimes of 5 existing dimes

`_(15)C_(2)` = get 2 dimes of 15 coins in total

`P = (_(5)C_(2))/(_(15)C_(2))`

Where,

`_(5)C_(2)=(5!)/(2!(5-2)!)=(5.4.3!)/(2(3)!)=(5.4)/(2)=(20)/(2)=10`

`_(15)C_(2)=(15!)/(2!(15-2)!)=(15.14.13!)/(2(13)!)=(15.14)/(2)=(210)/(2)=105`

`P = (_(5)C_(2))/(_(15)C_(2))=(10)/(105)=0.095`

The probability that Dianna grabs two dimes is 0.095

Hope this helps!