# Moderate Probability Solved QuestionAptitude Discussion

 Q. $A$ and $B$ play a game where each is asked to select a number from 1 to 5. If the two numbers match, both of them win a prize. The probability that they will not win a prize in a single trial is:
 ✖ A. 1/25 ✖ B. 24/25 ✔ C. 20/25 ✖ D. 23/25

Solution:
Option(C) is correct

Total number of ways in which both of them can select a number each:

$=5\times 5$

$=25$

otal number of ways in which both of them can select a same number so that they both can win:

$=5 \text{ ways}$ [They bothe can select {(1,1),(2,2),(3,3),(4,4),(5,5)}]

Probability that they win the prize:

$=\dfrac{\text{Favourable Cases}}{\text{Total Cases}}$

$= \dfrac{5}{25}$

Probability that they do not win a prize:

$=1-\dfrac{5}{25}$

$=\dfrac{20}{25}$

## (7) Comment(s)

Anurag
()

Required number of ways in which they don't win = 5C1 * 4C1

(i.e. Selecting a number by first person from 5 numbers is 5C1 and selecting a number other than that is selecting a number from remaining 4 numbers which is 4C1).

So, Required probability should be = 5C1 * 4C1 / 25 = 20/25

Shravan
()

Deepak
()

Corrected, Thanks for bringing it up.

Priyank
()

it should be 4/5

Sireesh
()

In question, the numbers should be from 1 to 25 not 1-5

Lynn
()

There are 25 possible number combinations

As stated in the solution but there are 5

Winning combinations: 1,1 2,2 3,3 4,4 and 5,5 so the probability of not winning is 4/5.

Silpa
()

Could u tell me how the probablity that they win the prize is

$1 * 1/25 = 1/25$?

I am getting 4/5 as the answer