Q.The probability of obtaining even prime number on each die, when a pair of dice is rolled is :

With 13 spades among 52 cards, $P(\text{spade}) = \tfrac{13}{52} = \tfrac14$, so the answer is option (c).

Using the classical definition of probability,

$P(E) = \frac{\text{number of favourable outcomes}}{\text{total number of outcomes}}.$

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The even prime is $2$; needing $2$ on both dice gives $\tfrac16\times\tfrac16=\tfrac1{36}$.

The even prime number is $2$ (the only prime that is even). We want a $2$ on each die when a pair is rolled.

For one die, $P(\text{showing }2) = \dfrac{1}{6}$. The two dice are independent, so

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The probabilities of all the elementary (simple) events of a sample space always sum to $1$.

For a sample space $S=\{E_1,E_2,\dots,E_n\}$, the elementary events $E_1,E_2,\dots,E_n$ are mutually exclusive and exhaustive — exactly one of them occurs on every trial. Therefore their pro …