A person throws two fair dice. He wins Rs. , 15 for throwing a do… - Vidyadip

MCQ

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

A
$\frac{1}{4}$ loss
B
$2$ gain
C
$\frac{1}{2}$ gain
✓
$\frac{1}{2}$ loss

✓

Answer

Correct option: D.

$\frac{1}{2}$ loss

d

$Coin$	$+15$	$+12$	$-6$
$Probability$	$\frac{6}{{36}}$	$\frac{4}{{36}}$	$\frac{{26}}{{36}}$

Probability of doublet $=\frac{6}{36}$

Probability of sum of $9=\frac{4}{36}$

Other probability $=\frac{26}{36}$

Expected gain/loss $=15 \times \frac{6}{36}+12 \times \frac{4}{36}-6 \times \frac{26}{36}$

$=\frac{90}{36}+\frac{48}{36}-\frac{156}{36}=\frac{-1}{2}$

Hence correct answer is option $(D)$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

If $z$ is a non-real complex number, then the minimum value of $\frac{{\operatorname{l} m{z^5}}}{{{{\left( {lmz} \right)}^5}}}$ is

A ladder $5\ m$ in length is resting against vertical wall. The bottom of the ladder is pulled along the ground away from the wall at the rate of $1.5\,m/\sec $. The length of the highest point of the ladder when the foot of the ladder $4.0\,m$ away from the wall decreases at the rate of .......... $m/sec$

Consider a triangle $\mathrm{ABC}$ having the vertices $\mathrm{A}(1,2), \mathrm{B}(\alpha, \beta)$ and $\mathrm{C}(\gamma, \delta)$ and angles $\angle \mathrm{ABC}=\frac{\pi}{6}$ and $\angle \mathrm{BAC}=\frac{2 \pi}{3}$. If the points $\mathrm{B}$ and $\mathrm{C}$ lie on the line $\mathrm{y}=\mathrm{x}+4$, then $\alpha^2+\gamma^2$ is equal to....................

The minimum value of $2x + 3y,$ when $xy = 6,$ is

$\int\limits_0^{\frac{\pi }{2}} { {\frac{{4x\sin \,x\, + \,{x^2}\,\cos \,x}}{{2\sqrt {\sin \,x} }}} dx }$ is equal to

The order and degree of the differential equation ${\left[ {4 + {{\left( {\frac{{dy}}{{dx}}} \right)}^2}} \right]^{2/3}} = \frac{{{d^2}y}}{{d{x^2}}}$ are

The set $S = \left\{ {1,2,3, \ldots ,12} \right\}$ is to be partitioned into three sets $A,\,B,\, C$ of equal size . Thus $A \cup B \cup C = S$ અને $A \cap B = B \cap C = C \cap A = \emptyset $ . The number of ways to partition $S$ is

If $f'(x) = \sin (\log x)$ and $y = f\left( {\frac{{2x + 3}}{{3 - 2x}}} \right)$, then $\frac{{dy}}{{dx}} = $

Number of solutions of the equation ${\log _{\sqrt 3 }}\left( {{x^3} - 1} \right) = {\log _{\sqrt 3 }}\left( {x - 1} \right) + 2$ is (are)

Let $\triangle PQR$ be a triangle. Let $\vec{a}=\overline{Q R}, \vec{b}=\overline{R P}$ and $\vec{c}=\overline{P Q}$. If $|\vec{a}|=12,|\vec{b}|=4 \sqrt{3}$ and $\vec{b} \cdot \vec{c}=24$, then which of the following is (are) true?

$(A)$ $\frac{|\vec{c}|^2}{2}-|\vec{a}|=12$

$(B)$ $\frac{|\vec{c}|^2}{2}+|\vec{a}|=30$

$(C)$ $|\vec{a} \times \vec{b}+\vec{c} \times \vec{a}|=48 \sqrt{3}$

$(D)$ $\vec{a} \cdot \vec{b}=-72$