A man chooses1 card from 6. he tries again and chooses the same card out of 6 that he did the 1st time. Odds?

Question

he then does the very same thing again, picking the same card twice out of 6. However, the card he picks the first time twice is not the very same card he picked the second round twice. What are the odds of this happening the first round? What are the odds of this happening two rounds in a row?

Answer 1

Since the first card can be any card at all, the "probability " for the first card is 6/6 (100%). There are 6 cards total, so the probability that the second card matches is 1/6.

On the second go-round, he picks a different card. The probability that it won't match the first card are 5/6. The probability that the second card matches the first card are still 1/6.

To find the overall probability for this event, multiply all the probabilites:

1 * 1/6 * 5/6 * 1/6 = 5/216, or about 42.2 to 1 against doing this.

If the card on the second go-round can match the first go-round card, the third term becomes 6/6, to the overall probability would be 1/36, or 35:1 against.

Answer 2

1/6

Answer 3

The first time 1/6 x 1/6 = 1/12.

Second time = 1/432