You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Probability Distribution

In a game, a ...

Question

In a game, a man wins Rs. $100$ if he gets $5$ or $6$ on a throw of a fair die and loses Rs. $50$ for getting any other number on the die. If he decides to throw the die either till he gets a five or a six or to a maximum of three throws, then his expected gain/loss (in rupees) is :

\frac{400}{9}

loss

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

\frac{400}{3}

loss

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

\frac{400}{3}

gain

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

0

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

Open in App

Solution

The correct option is D $0$
$A :$ Event that $5$ or $6$ appear on die.
$B :$ Event that any other number appear on die.
Therefore, following events are possible.
$A, B A, B B A, B B B$
$X :$ Random variable denoting the amount won.
$\begin{matrix} X & + 100 & + 50 & 0 & - 150 P(X) & \frac{1}{3} & \frac{2}{9} & \frac{4}{27} & \frac{8}{27} \end{matrix}$

$E (X) = \frac{100}{3} + \frac{100}{9} + 0 - \frac{1200}{27} = 0$

Suggest Corrections

Similar questions

Q. In a game, a man wins Rs.

1000

if he gets an even number

\geq 4

on a fair die and loses Rs.

200

for getting any other number on the die. If he decides to throw the die until he wins or maximum of three times, then his expected gain/loss (in Rupees) is

In a game, a man wins a rupee for a six and losses a rupee for any other number when a fair die is thrown. The man decide to throw a die thrice but to quit as and when he gets a six. Find the expected value of the amount he wins/loses.

Q. In a game, a man wins Rs.

5

for getting a number greater than

4

and loses Rs.

1

otherwise, when a fair die is thrown. The man decided to throw a die thrice but to quit as and when he gets a number greater than

4

. Find the expected value of the amount he wins/loses.

Q. A person throws two fair dice. He wins Rs.

15

for throwing a doublet (same numbers on the two dice), wins Rs.

12

when the throw results in the sum of

9

, and loses Rs.

6

for any other outcome on the throw. Then the expected gain/loss (in Rs.) of the person is :

Q. A person throws two fair dice. He wins Rs.

15

for throwing a doublet (same numbers on the two dice), wins Rs.

12

when the throw results in the sum of

9

, and loses Rs.

6

for any other outcome on the throw. Then the expected gain/loss (in Rs.) of the person is :

Join BYJU'S Learning Program

In a game, a man wins Rs. 100 if he gets 5 or 6 on a throw of a fair die and loses Rs. 50 for getting any other number on the die. If he decides to throw the die either till he gets a five or a six or to a maximum of three throws, then his expected gain/loss (in rupees) is :

The correct option is D 0A: Event that 5 or 6 appear on die. B: Event that any other number appear on die. Therefore, following events are possible. A,BA,BBA,BBB X: Random variable denoting the amount won. X+100+500−150P(X)1329427827 E(X)=1003+1009+0−120027=0

In a game, a man wins Rs. $100$ if he gets $5$ or $6$ on a throw of a fair die and loses Rs. $50$ for getting any other number on the die. If he decides to throw the die either till he gets a five or a six or to a maximum of three throws, then his expected gain/loss (in rupees) is :