Final answer:
When drawing two cards from a standard 52-card deck, the probability of drawing clubs both times is 0.0588 or 5.88% without replacement, and 0.0625 or 6.25% with replacement.
Step-by-step explanation:
The probability calculation for selecting cards from a deck can be performed by considering the favorable outcomes over the total possible outcomes. To calculate the probability of selecting a club from a deck of cards, we distinguish between the cases of sampling with replacement and sampling without replacement.
a. Without Replacement
For sampling without replacement, the probability that the first card is a club is 13/52 (since there are 13 clubs in a 52-card deck). If the first card is indeed a club, there are now 12 clubs remaining out of 51 cards. Thus, the probability that the second card is also a club is 12/51. Multiplying these probabilities together gives us: (13/52) × (12/51) = 0.0588 or 5.88% when rounded to three decimal places.
b. With Replacement
For sampling with replacement, the deck is reset after each draw, meaning the probability of drawing a club remains 13/52 for both draws. Therefore, the probability of drawing two clubs in a row with replacement is (13/52) × (13/52) = 0.0625 or 6.25% when rounded to three decimal places.