In a business venture, a man can make a profit of $\displaystyle 50,000$ or incur a loss of $\displaystyle 20,000$. The probabilities of making profit or incurring loss, from the past experience, are known to be $\displaystyle 0.75$ and $\displaystyle 0.25$ respectively. What is his expected profit?

If $\displaystyle P(A) = \frac{1}{2}$, $\displaystyle P(B) = \frac{1}{3}$, $\displaystyle P(A \cap B) = \frac{1}{4}$, then the value of $\displaystyle P(A' \cup B')$ is

Two dice are thrown simultaneously. Find the probability that the sum of digits on the two dice would be 8 or more.

A number is selected from the first 20 natural numbers. Find the probability that it would be divisible by 3 or 7.

A father had three sons namely, Kailash, Harish and Prakash. All are above 65 years in age. Prakash happens to be the eldest while Kailash as youngest. As per the health history, it is estimated that the probability that Kailash survives another 5 years is $\displaystyle \frac{4}{5}$, Harish survives another 5 years is $\displaystyle \frac{3}{5}$ and Prakash survives another 5 years is $\displaystyle \frac{1}{2}$. The probabilities that Kailash and Harish survive another 5 years is 0.46, Harish and Prakash survive another 5 years is 0.32 and Kailash and Prakash survive another 5 years is 0.48. The probability that all three sons survive another 5 years is 0.26. What shall be the probability that at least one of them survives another 5 years?

In a class, there are 15 boys and 10 girls. Three students are selected at random. The probability that 1 girl and 2 boys are selected is

Two cards are drawn from a pack of 52 cards. The probability that one is a spade and one is a heart; is