Out of the given 25 consecutive position integers, three integers are drawn. If the least integer among given 25 integers is an odd number, then the probability that the sum of the three integers drawn is an even number is

If three dice are thrown at a time, then the probability of getting the sum of the numbers on them as a prime number is

Three companies $C_1, C_2, C_3$ produce car tyres. A car manufacturing company buys $40 \%$ of its requirement from $C_1, 35 \%$ from $C_2$ and $25 \%$ from $C_3$. The company knows that $2 \%$ of the tyres supplied by $C_1, 3 \%$ by $C_2$ and $4 \%$ by $C_3$ are defective. If a tyre chosen random from the consignment received is found defective then, the probability that it was supplied by $C_2$ is

If the mean and variance of a binomial distribution are $\frac{4}{3}$ and $\frac{10}{9}$ respectively, then $P(X \geq 6)=$