Refer to the tree diagram. You are playing a game. You have chosen a card that is an ace, and have won $100. However, you are told that if you chose another card, you will receive $50 more if it is not an ace but you must give back the $100 if it is an ace. Why would choosing another card be a good decision? (1 point) Responses There is a 96% probability that the second card is not an ace. There is a 96% probability that the second card is not an ace. There is a 94% probability that the second card is not an ace. There is a 94% probability that the second card is not an ace. There is an 83% probability that the second card is not an ace. There is an 83% probability that the second card is not an ace. There is a 92% probability that the second card is not an ace. There is a 92% probability that the second card is not an ace. Skip to navigation

Answer 1

To determine why choosing another card might be a good decision, we should consider the probabilities involved in drawing another card.

If you have already drawn an ace and won $100, there are generally 52 cards in a standard deck, out of which 4 are aces. If you have already drawn one ace, that leaves 51 cards in total, with 3 of those being aces.

Calculating the probability of not drawing an ace on the next card:

• The number of non-aces left = 51 total cards - 3 aces = 48 non-aces.
• Therefore, the probability of drawing a non-ace on the second card is \( \frac{48}{51} \), which is approximately \( 0.941 \) or \( 94% \).

Since there is a 94% probability of drawing a non-ace (which would give you an additional $50), and only a 6% probability of drawing another ace (which would cause you to lose the $100), the expected value of drawing another card is positive.

Thus, choosing another card would be a good decision because there is a 94% probability that the second card is not an ace, allowing you to increase your total winnings by $50 rather than losing the $100.

In conclusion, the correct choice is: There is a 94% probability that the second card is not an ace.