Question

An urn contains 6 balls that are numbered 1 through 6. Suppose you draw 4 balls randomly in sequence, each time the replacing the ball selected previously. Let X be the maximum of the 4 numbers chosen. Find the probabilities P(X=k) for all possible values k.

Answer 1

The probabilities P(X=k) for all possible values k in the given scenario of drawing balls randomly with replacement from an urn of numbered balls.

Step-by-step explanation:

To find the probabilities P(X=k) for all possible values k, we need to consider the maximum value of the 4 numbers chosen from the urn.

Since each ball is replaced after it's drawn, the maximum value can only be the highest number in the urn, which is 6.

Therefore, the probabilities P(X=k) are:

• P(X=1) = 0
• P(X=2) = 1/6
• P(X=3) = 1/6
• P(X=4) = 1/6
• P(X=5) = 1/6
• P(X=6) = 2/6