Chapter 5.1, Problem 12E

(a)

To determine

To explain to a gambler what is wrong with this reasoning given in the question.

Explanation of Solution

The gambler observes five consecutive reds occur and bets heavily on black at the next spin. Then the gambler given the reason for the same that black is “due by law of averages”. The gambler was wrong with his reasoning because a spin is not dependent on the previous spins and thus on the spin after five consecutive spins it will still be equally likely to spin red as it is to spin black.

(b)

To determine

To find out is the gambler right or wrong and explain why.

Answer to Problem 12E

The gambler was wrong.

Explanation of Solution

After explaining, the gambler assumes that the next card dealt in the same hand is equally likely to be red or black. But the gambler was wrong in his assumption. The gambler is wrong, because the five red cards that have been dealt are no longer in the deck of cards. Thus the deck of cards then contains more black cards than red cards, making it more likely to be dealt a black card.