Question
Marco draws a card and replaces it 10 times from a standard deck of 52 cards. He draws 8 red cards and 2 black cards. What is the theoretical probability that he will draw a red card on his 11th draw?
Responses
A
1 4
B
1 2
C
2 3
D
Answers
GPT-4o mini
The theoretical probability of drawing a red card from a standard deck of 52 cards remains constant, regardless of the previous draws, since the card is replaced each time.
In a standard deck of 52 cards, there are 26 red cards (hearts and diamonds) and 26 black cards (clubs and spades).
The probability of drawing a red card is calculated as follows:
\[
P(\text{red}) = \frac{\text{Number of red cards}}{\text{Total number of cards}} = \frac{26}{52} = \frac{1}{2}
\]
Therefore, the theoretical probability that Marco will draw a red card on his 11th draw is:
\[
\frac{1}{2}
\]
The correct response is:
B \( \frac{1}{2} \)
In a standard deck of 52 cards, there are 26 red cards (hearts and diamonds) and 26 black cards (clubs and spades).
The probability of drawing a red card is calculated as follows:
\[
P(\text{red}) = \frac{\text{Number of red cards}}{\text{Total number of cards}} = \frac{26}{52} = \frac{1}{2}
\]
Therefore, the theoretical probability that Marco will draw a red card on his 11th draw is:
\[
\frac{1}{2}
\]
The correct response is:
B \( \frac{1}{2} \)