Question: In United States currency, a nickel is worth 5 cents, a penny is worth 1 cent, and a dime is worth 10 cents. 100 cents equals one dollar. If a hand purse contains 6 nickels, 5 pennies and 4 dimes, what is the probability of picking a coin other than a nickel twice in a row if the first coin picked is not put back?

1. 8/25
2. 12/35
3. 13/35
4. 9/25
5. 17/25

Correct Answer: B

Solution and Explanation:
Approach Solution 1:
In this case it would be easier to calculate the probability in direct way: non−nickel/all∗non−nickel−1/all−1= 9/15∗8/14= 12/35.

The problem in your solution is that the opposite probability of two non-nickel coins in a row is not two nickel in a row, it's two nickels in a row plus either of two coins from two is nickel, (so basically the probability of at least one nickel from two picks): 6/15∗5/14+2∗6/15∗9/14= 23/35

P=1−23/35= 12/35

Approach Solution 2:
There are 15 coins total. 5P + 4D = 9 coins that give me the desired outcome.

For the first pick, total outcomes = 15. Desired outcomes = 9. Probability of desired outcome is 9/15: We have 9 chances out of 15 total to get a D or a P.

The total number of coins is now 14. And there is one fewer coin in the desired group. So for second pick, probability of desired outcome is 8/14
9/15 *8/14= 12/35

Approach Solution 3:
probability of picking a coin other than a nickel (first turn)= 9/15
probability of picking a coin other than a nickel (first turn)= 8/14

P= (9/15)*(8/14)= (3/5)*(4/7)= 12/35

“In United States currency, a nickel is worth 5 cents”- is a topic of the GMAT Quantitative reasoning section of GMAT. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.

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