I am having troubles with the question:
You have a standard deck of $52$ playing cards ($13$ of each suit). You draw a hand of the top $18$ of them. Spades are one of the four suits. What is the expected value of the number of spades you draw?
For my approach I calculate the individual probabilities for every event of drawing a spades as so:
Let $P_i$ be the probability that $i$ spades drawn.
So naturally calculating the Expected value would as follows:
$$\sum_{i =0}^{n = 13}i\cdot P_i$$
However this task is tedious and leaves the question of where the remaining $5$ cards in the hand adds up to the equation.
Am I even thinking in the right direction? Is there a better way to calculate this?
Best Answer
It is easy to understand.. Since there are 4 suits, Probability of any random card being a spade is $${1\over 4}$$ So the expected number of spades are $$18\times {1\over 4}=4.5$$