Final answer:
The probability of drawing a card that is either a jack, a three, a club, or a diamond from a standard 52-card deck is approximately 0.5769 or 57.69% after considering overlapping outcomes.
Step-by-step explanation:
The question asks for the probability of drawing a card that is either a jack, a three, a club, or a diamond from a standard 52-card deck. To calculate this, we need to consider the number of favorable outcomes and divide by the total number of possible outcomes.
- Number of jacks in the deck: 4 (J of hearts, J of spades, J of clubs, J of diamonds)
- Number of threes in the deck: 4 (3 of hearts, 3 of spades, 3 of clubs, 3 of diamonds)
- Number of clubs in the deck: 13 (all clubs, including the J and 3 of clubs which have been counted already)
- Number of diamonds in the deck: 13 (all diamonds, including the J and 3 of diamonds which have been counted already)
To avoid counting the J and 3 of clubs and diamonds twice, we subtract 2 from the total count of clubs and diamonds.
Favorable outcomes = 4 jacks + 4 threes + (13 clubs - 1 jack - 1 three) + (13 diamonds - 1 jack - 1 three) = 8 + 11 + 11 = 30
So, the probability is 30 favorable outcomes out of 52 possible outcomes, which is ≈ 0.5769 or about 57.69% when converted to a percentage.