Answer: 32.69
Explanation:
To calculate the probability of winning the game (and winning $10) when drawing a card randomly from a standard deck of playing cards, you need to determine the number of favorable outcomes (winning cards) and divide it by the total number of possible outcomes (all cards in the deck).
There are 52 cards in a standard deck, and it contains 4 suits: hearts, diamonds, clubs, and spades. Each suit has 13 cards, including one ace.
To win the game, you can either draw a spade or an ace. Let's calculate the number of winning cards:
There are 13 spades in the deck.
There are 4 aces in the deck (one ace in each suit).
So, there are a total of 13 spades + 4 aces = 17 winning cards.
Now, let's calculate the probability of winning:
Probability of winning = (Number of winning cards) / (Total number of cards)
Probability of winning = 17 / 52
Simplify this fraction by dividing both the numerator and denominator by their greatest common divisor (which is 1 in this case):
Probability of winning = 17 / 52
This is the probability of winning the game when drawing a card randomly from a standard deck. To convert it to a decimal or percentage:
Probability of winning ≈ 0.3269 or approximately 32.69%
So, the probability that you will win the game (and $10) is approximately 32.69%.