Question

Students are playing a game similar to blackjack (with a standard 52 card deck)- trying to get as close to 21 points without going over. The ace is only worth 1 point and each face card is worth 10 points, the remaining cards have face value. Player A draws a eight and a nine. Player B draws a four and a jack. If Player A next draws a two, what is the probability of Player B winning the round?

Answer 1

Player B has an 8.16% chance of drawing a seven from the remaining 49 cards in the deck to win the round after Player A's total reached 19.

Step-by-step explanation:

Probability of Player B Winning

Player A has an eight and a nine, totalling 17 points, and then draws a two, bringing their total to 19. Player B has a four and a jack, which totals 14 points.

For Player B to win, they must draw a card that brings their total to higher than 19 but not over 21. This means Player B can only win if they draw a seven, which gives them 21 points. Since there are four sevens in a standard 52-card deck and three cards have already been drawn without replacement, there are 49 cards left.

This simplifies to approximately \(0.0816\), or an 8.16% chance that Player B will win the round.