Probability of drawing a 10, then a 2, then a Jack from a deck of 52 cards without replacement. Express your answer as a reduced fraction or as a decimal rounded to three significant figures.

Answer 1

The probability of drawing the initial 10 is 4 (the number of 10s in the deck) out of 52 (the number of cards in the deck). This can be reduced by 4 to make 1 out of 13. Drawing a two would then be 4 out of 51, since we didn't replace the card. Finally, drawing a Jack from the remainder of the deck has a probability of 4 out of 50, or 2 out of 25. We multiply these three probabilities to find the probability of these three events happening in succession. 1/13 x 4/51 x 2/25 = (4 x 2 x 1)/(13 x 51 x 25) = 8/16575. This fraction cannot be reduced, and the corresponding decimal (0.0004826...) would be rounded to 0.000483, or 4.83 x 10^-4.