Question

QUESTION 4

After removing all of the clubs from a deck of cards, you are left with a 39 card deck with Hearts, Diamonds, and Spades. Answer the following question assuming that after each draw of a card, that card is returned to this deck and reshuffled.
What is the probability (in decimal, not fraction) of drawing four red cards in a row (with replacement)? Give your answer in decimal form, rounded to 4 decimal places.

Answer 1

The probability of drawing four red cards in a row with replacement from a 39-card deck is approximately 0.2430.

Step-by-step explanation:

To find the probability of drawing four red cards in a row with replacement, we need to calculate the probability of drawing a red card at each step and multiply them together. Firstly, let's determine the number of red cards in the 39-card deck. Since each suit has 13 cards and we removed clubs, the remaining red cards are diamonds and hearts, which have a total of 26 cards (13 each).

The probability of drawing a red card on the first draw is 26/39. Since we are replacing the card after each draw, the probability remains the same for subsequent draws. Therefore, the probability of drawing four red cards in a row is (26/39) * (26/39) * (26/39) * (26/39).

Calculating this probability gives us approximately 0.2430 (rounded to 4 decimal places).

Answer 2

The probability of drawing four red cards in a row (with replacement)is 0.1975

Step-by-step explanation:

Assuming we have a standard card deck, we'll have this color distribution:

• Spades : Black
• Clubs : Black
• Diamonds : Red
• Hearts : Red

In consequence, if we remove all of the clubs from the deck, we will have 26 red cards out of 39 cards left.

Now, let's recall that the formula of probability is:

Probability = Number of favorable outcomes/Total number of possible outcomes

Replacing with the values we know:

• Probability of drawing a 1st red card = 26/39 = 2/3
• We return the 1st card to the deck, reshuffle and draw a new card:
• Probability of drawing a 2nd red card = 2/3
• We return the 2nd card to the deck, reshuffle and draw a new card:
• Probability of drawing a 3rd red card = 2/3
• We return the 3rd card to the deck, reshuffle and draw a new card:
• Probability of drawing a 4th red card = 2/3

Therefore,

Probability of drawing four red cards in a row (with replacement):

2/3 * 2/3 * 2/3 * 2/3 = 16/81

16/81 = 0.1975