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A pair of dice is thrown. Find the probability of getting a sum of

    \[\mathbf{10}\]

or more, if

    \[\mathbf{5}\]

appears on the first die
CBSE | Class 10 | Exercise 13.2 | Selina | Statistics and Probability
A pair of dice is thrown. Find the probability of getting a sum of

    \[\mathbf{10}\]

or more, if

    \[\mathbf{5}\]

appears on the first die

Solution:

In throwing a dice, total possible outcomes

    \[=\text{ }\left\{ 1,\text{ }2,\text{ }3,\text{ }4,\text{ }5,\text{ }6 \right\}\]

So

    \[,\text{ }n\left( S \right)\text{ }=\text{ }6\]

For two dice

    \[,\text{ }n\left( S \right)\text{ }=\text{ }6~x\text{ }6\text{ }=\text{ }36\]

Favorable cases where the sum is 10 or more with

    \[5\text{ }on\text{ }{{1}^{st}}~die\text{ }=\text{ }\left\{ \left( 5,\text{ }5 \right),\text{ }\left( 5,\text{ }6 \right) \right\}\]

Event of getting the sum is

    \[10\]

or more with

    \[5\text{ }on\text{ }{{1}^{st}}~die\text{ }=\text{ }n\left( E \right)\text{ }=\text{ }2\]

Hence, the probability of getting a sum of

    \[10\]

or more with

    \[5\text{ }on\text{ }{{1}^{st}}~die\text{ }=\text{ }n\left( E \right)/\text{ }n\left( S \right)\text{ }=\text{ }2/\text{ }36\text{ }=\text{ }1/18\]

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