**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!