Final answer:
The probability that the first card drawn is a heart, the second is a red card, and the third is a queen, with each draw occurring with replacement from a standard deck, is 0.0120 or 1.20%, rounded to four decimal places.
Step-by-step explanation:
The question asks for the probability of three specific events happening in sequence when drawing cards from a standard deck with replacement. To find the probability of drawing a heart as the first card, we consider that there are 13 hearts in a 52-card deck. Hence, the probability (P) for this event is P(heart) = 13/52.
For the second event, drawing a red card, there are 26 red cards (hearts and diamonds) in the deck. Therefore, the probability (P) for this event is P(red card) = 26/52.
Finally, for the third event, drawing a queen, there are 4 queens in the deck, one in each suit. So, the probability (P) for this event is P(queen) = 4/52.
Because each draw is with replacement, the previous draws do not affect the probabilities of the subsequent draws. We can find the overall probability by multiplying the probabilities of the individual events:
- P(heart) × P(red card) × P(queen) = (13/52) × (26/52) × (4/52).
- This simplifies to (13×26×4)/(52×52×52).
- Calculating this gives a probability of 0.0120 or 1.20% when rounded to four decimal places.