A-Level Mathematics Question Analysis Topic: Mathematics - Probability
Exam Question:
Three cards are drawn successively with replacement from a well shuffled pack of 52 cards. Find the probability distribution of the number of spades. Hence find the mean of the distribution.
Answer:
For A-Level Mathematics, you should know:
P(0 spades): 3/4 x 3/4 x 3/4 = 27/64
P(1 spade): 3 x 1/3 x 3/4 x 3/4 = 27/64
P(2 spades) 3 x 1/4 x 1/4 x 3/4 = 9/64
P(3 spades) 1/4 x 1/4 x 1/4 = 1/64
Total: 27/64 + 27/64 + 9/64 + 1/64 = 64/64 = 1
In other words,
the probabilty of getting a spade is the same no matter the pick, since the cards are replaced after every pick. This makes them independent events.
The mean of the distribution is ∑xiP(X=xi) = 3/4.
Work hard for your A-Level Mathematics examination!
End of analysis. Great!