Two cards are drawn without replacement from a deck of 52 cards.
a. What is the probability of drawning 2 aces?
b. What are the odds in favour of drawing 2 honour cards? (A, K, Q, J, 10)
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The probability of drawing the first ace is 4/52. Without replacement, the probability of drawing the second ace is 3/51. (Do you understand why?) The probability of events all happening is found by multiplying the individual probabilities.
The probability of drawing the first "honour card" is 20/52. Use the same methodology as in the above problem.
I hope this helps.
A die a rolled
An even is obtained
To find the probability of drawing 2 aces, we need to determine the number of favorable outcomes (drawing two aces) and the total number of possible outcomes (drawing two cards without replacement from a deck of 52 cards).
a. Probability of drawing 2 aces:
The first card can be any of the 52 cards in the deck since we haven't drawn any card yet. However, we specifically want an ace, so there are 4 aces in the deck. Therefore, the probability of drawing an ace as the first card is 4/52 (since there are 4 favorable outcomes out of 52 total outcomes).
Once the first card has been drawn and not replaced, there are now 51 cards left in the deck. Since the first card was an ace, there are now 3 aces left in the deck. So, the probability of drawing an ace as the second card is 3/51.
To find the probability of both events occurring (drawing 2 aces), we multiply the probabilities together:
Probability of drawing 2 aces = (4/52) * (3/51) = 12/2652 ≈ 0.0045 ≈ 0.45%
Therefore, the probability of drawing 2 aces is approximately 0.45%.
To determine the odds in favor of drawing 2 honor cards, we need to find the number of favorable outcomes (drawing two honor cards, which can be any combination of A, K, Q, J, or 10) and the number of unfavorable outcomes (drawing anything other than two honor cards).
b. Odds in favor of drawing 2 honor cards:
There are 4 honor cards (A, K, Q, J, 10) in each suit, so there are a total of 20 honor cards in the deck.
The first card can be any of the 52 cards, but for an honor card, there are 20 honor cards out of the total 52 cards. Therefore, the probability of drawing an honor card as the first card is 20/52.
Once the first card has been drawn and not replaced, there are now 51 cards left in the deck. Since the first card was an honor card, there are now 19 honor cards left in the deck. So, the probability of drawing an honor card as the second card is 19/51.
To find the odds in favor, we divide the probability of the favorable outcome by the probability of the unfavorable outcome (1 minus the probability of the favorable outcome):
Odds in favor of drawing 2 honor cards = (20/52) * (19/51) / (1 - (20/52) * (19/51))
Simplifying this expression, we get:
Odds in favor of drawing 2 honor cards = 190/2652 ≈ 0.0716 ≈ 7.16%
Therefore, the odds in favor of drawing 2 honor cards are approximately 7.16%.