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

Answer:

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