Probability
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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

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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
 ()

Ans is 20/25. Please check


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