A die is thrown once. Find the probability of getting a number: \[\left( \mathbf{i} \right)\] less than \[\mathbf{3}\] \[\left( \mathbf{ii} \right)\] greater than or equal to \[\mathbf{4}\]

Solution:

We know that,

In throwing a dice, total possible outcomes \[=\text{ }\left\{ 1,\text{ }2,\text{ }3,\text{ }4,\text{ }5,\text{ }6 \right\}\]

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

\[\left( i \right)\] On a dice, numbers less than \[3\text{ }=\text{ }\left\{ 1,\text{ }2 \right\}\]

So\[,\text{ }n\left( E \right)\text{ }=\text{ }2\]

Hence, probability of getting a number less than \[3\text{ }=~n\left( E \right)/\text{ }n\left( S \right)\text{ }=\text{ }2/6\text{ }=\text{ }1/3\]

(ii) On a dice, numbers greater than or equal to \[4\text{ }=\text{ }\left\{ 4,\text{ }5,\text{ }6 \right\}\]

So\[,\text{ }n\left( E \right)\text{ }=\text{ }3\]

Hence, probability of getting a number greater than or equal to \[4\text{ }=\text{ }n\left( E \right)/\text{ }n\left( S \right)\text{ }=\text{ }3/6\text{ }=\text{ }1/2\]4