Question

In a box are six balls with the numbers 2, 6, 7, 13, 23, 34.

(a) (2 points) You draw four balls at the same time. What is the probability that two of them are prime numbers?

(b) (2 points) Draw a ball, put it back in the box, and draw another ball. Let A be the event that the first ball is even, and let B be the event that the product of the two numbers on the two balls is even. Are A and B independent?

(c) (2 points) Draw again two balls in the ways as in (b). Let X be the random variable assigning to the outcome the sum of the numbers on the two balls. What is P(X ≥ 50)? 1

(d) (2 points) Remove all balls from the box except 7 and 13. Draw again two balls from the box in the same way as (b) and let X be defined as in (c). Calculate its expected value.

Answer 1