Aptitude 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:

\(=1-\dfrac{5}{25}\)

\(=\dfrac{20}{25}\)

**Anurag**

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**Shravan**

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Ans is 20/25. Please check

Corrected, Thanks for bringing it up.

**Priyank**

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it should be 4/5

**Sireesh**

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

**Lynn**

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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**

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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

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