A child is drawing cards from a standard deck of cards, one at a time, observing the color, replacing the card, and shuffling. He observes that 7 consecutive outcomes with a black card have occurred and thinks the next one will be red because "red is due to occur.”Is the child’s reasoning correct?
Answer
A
Yes, it is unlikely that the child will draw a black card 7 times in a row, so red must be due.
B
No, if a black card is drawn 7 times in a row, the deck must be unfairly weighted toward black.
C
Yes, the child has to begin drawing red cards in order for the probability of red and black to get back to 0.5.
D
No, red and black outcomes are equally likely, so the probability of drawing a black card is the same regardless of the outcomes of the prior draws.
Explanation
The card is replaced and the deck is shuffled after each draw, so every draw is independent of the previous ones. A standard deck has equal numbers of red and black cards, making the chance of black 0.5 on the next draw, just as it was before the streak. Red is not “due”; D correctly says the probability is unchanged by prior draws.
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