A deck of playing cards has 52 cards. A card is drawn, replaced, and then this process is repeated three more times. What is the probability of getting a heart on the first draw, a spade on the second draw, a club on the third draw, and a diamond on the fourth draw?
Options
A
B
C
D
Answer & Analysis
Answer
B
Analysis
Question Analysis
This question involves calculating the probability of four independent events that occur during successive card draws with replacement.
The main focus is on determining the probability of drawing a specific suit in each draw and applying the multiplication rule for independent events to find the combined probability of the given sequence of draws.
Key Concept Explanation
Each card draw with replacement is an independent event because the deck is restored to its original state after each draw, and the outcome of one draw does not affect the others.
For multiple independent events , , , and , the probability of all of them occurring in a specific order is .
In a standard deck of 52 cards, each suit has 13 cards, so the probability of drawing a particular suit in a single draw is .
Step-by-Step Solution
Calculate the probability of each draw:
The probability of getting a heart on the first draw, .
The probability of getting a spade on the second draw, .
The probability of getting a club on the third draw,
Want More Practice Questions?
Access thousands of practice questions with detailed explanations on Scholardog.