A and B play a game where each is asked to select a number from 1 to 25. If the numbers selected by A and B match, both of them win a prize. The probability that they win their third prize on $5^{t h}$ game is equal to:

\frac{6. (24)^{2}}{(25)^{5}}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

\frac{6. (21)^{2}}{(25)^{5}}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{(24)^{2}}{(25)^{2}}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{6. (24)^{2}}{(25)^{4}}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $\frac{6. (24)^{2}}{(25)^{5}}$
Probability of winning the prize in single game
= probability of getting {(1, 1), (2, 2), ………… (25, 25)}
$= \frac{25}{25 \times 25} = \frac{1}{25}$
Probability(3rd prize in 5th game)
Probability (two prize in first 4 games) and prize in $5^{t h}$ game
$=^{4} C_{2} {(\frac{1}{25})}^{2} {(\frac{24}{25})}^{2} \times \frac{1}{25} = \frac{6 \times (24)^{2}}{(25)^{5}}$

Suggest Corrections

Similar questions

Q. A and B play a game where each is asked to select a number from

1

25

. 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

Arjit and Karan play a game where each one 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:

Q. X and Y plays a game in which they are asked to select a number from

21 - 50

. If the two number match both of them wins a prize. Find the probability that they will not win a prize in the single trial.

Q. In a lottery, a person chooses six different numbers at random from 1 to 20, and if these six numbers match with six number already fixed by the lottery committee, he wins the prize. What is the probability of winning the prize in the game?

A

and

B

play a match in which the chances of their winning a game is

\frac{1}{4}

for both of them and

\frac{1}{2}

is the probability that match is being drawn. Match is finished as soon as either player wins two games. Find the probability that the match will be finished in

4

or less games.

Join BYJU'S Learning Program

A and B play a game where each is asked to select a number from 1 to 25. If the numbers selected by A and B match, both of them win a prize. The probability that they win their third prize on 5th game is equal to:

The correct option is A 6.(24)2(25)5 Probability of winning the prize in single game = probability of getting {(1, 1), (2, 2), ………… (25, 25)} =2525×25=125 Probability(3rd prize in 5th game) Probability (two prize in first 4 games) and prize in 5th game =4C2(125)2(2425)2×125=6×(24)2(25)5

A and B play a game where each is asked to select a number from 1 to 25. If the numbers selected by A and B match, both of them win a prize. The probability that they win their third prize on $5^{t h}$ game is equal to: