Your mom is a sporting person, so when it's close to your bedtime, she will have a contest with you to see if you get to stay up an extra half-hour to play a computer game. You get to draw a card from a well-shuffled deck. If you draw a face card, an ace, or any heart, she'll "have a heart" and let you stay up. If you draw any other card, you lose and go ahead to bed. Who has the best chance of winning, you or your Mom?

Question

Your mom is a sporting person, so when it's close to your bedtime, she will have a contest with you to see if you get to stay up an extra half-hour to play a computer game. You get to draw a card from a well-shuffled deck. If you draw a face card, an ace, or any heart, she'll "have a heart" and let you stay up. If you draw any other card, you lose and go ahead to bed. Who has the best chance of winning, you or your Mom?

Answer 1

hearts = 13

aces = 4
face cards = 12
total = 29
but we counted AH, JH, QH, KH, twice
so the actual count = 29-4 = 25

prob(staying up) = 25/52
prob(going to bed) = 1 - 25/52 = 27/52

so what do you think?

Answer 2

mom has a higher chance of winning

Answer 3

To determine who has the best chance of winning in this scenario, we need to calculate the probabilities for both you and your Mom.

Let's analyze the probabilities step by step:

1. Total number of cards: A standard deck consists of 52 cards.
- Number of heart cards: There are 13 cards in a deck (Ace, 2-10, Jack, Queen, and King).
- Number of face cards: There are 12 face cards in a deck (Jack, Queen, and King of each suit).
- Total number of cards favorable to you: 3 (Face cards) + 4 (Aces) + 13 (Hearts) = 20
- Number of cards unfavorable to you: 52 - 20 = 32

2. Probability for you to win: The probability of drawing a card favorable to you is calculated by dividing the number of favorable outcomes by the total number of outcomes.
- Probability for you to win = Number of cards favorable to you / Total number of cards
- Probability for you to win = 20 / 52 ≈ 0.3846 (rounded to four decimal places)

3. Probability for your Mom to win: The probability for your Mom to win would be the complementary probability of you winning.
- Probability for your Mom to win = 1 - Probability for you to win
- Probability for your Mom to win = 1 - 0.3846 ≈ 0.6154 (rounded to four decimal places)

Therefore, based on the calculations, your Mom has a slightly higher chance of winning this bedtime contest. Her probability of winning is approximately 0.6154, while your probability of winning is approximately 0.3846.