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Standard XII

Mathematics

Probability Distribution

A person thro...

Question

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 :

2

gain

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\frac{1}{2}

loss

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\frac{1}{2}

gain

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\frac{1}{4}

loss

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Solution

The correct option is B $\frac{1}{2}$ loss
$\begin{matrix} X & + 15 & + 12 & - 6 P (X) & \frac{1}{6} & \frac{1}{9} & \frac{13}{18} \end{matrix}$

$E (X) = 15 \times \frac{1}{6} + 12 \times \frac{1}{9} - 6 \times \frac{13}{18} = - \frac{1}{2}$
So, expection is $\frac{1}{2}$ with a loss

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Won't we consider all loses in this ?

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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 :

The correct option is B 12 lossX+15+12−6P(X)16191318 E(X)=15×16+12×19−6×1318=−12 So, expection is 12 with a loss

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 :

The correct option is B $\frac{1}{2}$ loss
$\begin{matrix} X & + 15 & + 12 & - 6 P (X) & \frac{1}{6} & \frac{1}{9} & \frac{13}{18} \end{matrix}$

$E (X) = 15 \times \frac{1}{6} + 12 \times \frac{1}{9} - 6 \times \frac{13}{18} = - \frac{1}{2}$
So, expection is $\frac{1}{2}$ with a loss