Question

Find the probability of the events given in Question 2 [ (i) (a) a prime number (b) not a prime number. (ii) (a) a number greater than 5 (b) a number not greater than 5.].

Answer 1

When a die is thrown, there are total six outcomes, i.e., $1, 2, 3, 4, 5$ and $6$.
(i) (a) $2, 3, 5$ are prime numbers.
So there are $3$ outcomes out of $6$.
Therefore, probability of getting a prime number = $\frac{3}{6}$ = $\frac{1}{2}$

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(b) $1, 4, 6$ are not the prime numbers.
So there are $3$ outcomes out of $6$.
Therefore, probability of getting a prime number = $\frac{3}{6}$ = $\frac{1}{2}$

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(ii) (a) Only $6$ is greater than $5$.
So there is one outcome out of $6$.
Therefore, probability of getting a number greater than $5$ = $\frac{1}{6}$
(b) Numbers not greater than $5$ are $1, 2, 3, 4$ and $5$.
So there are $5$ outcomes out of $6$.
Therefore, probability of not getting a number greater than $5$ = $\frac{5}{6}$