Question

You are choosing between 2 different card games. In the first game, every time a face card is selected from the deck randomly, you win. In the second game, every time a heart is chosen, you win. Which game should you choose and why?

Answer 1

There are $52$ cards in a deck out of which $12$ are face card and $13$ are heart.

Let us consider two events $A$ and $B$ such that

$A=$ Selecting a face card

$B=$ Choose a heart card

Now probability of getting $A$ is $P(A)=\frac{12}{52}$

And probability of getting $B$ is $P(B)=\frac{13}{52}$

So hare we see that $P(B)>P(A)$ .

Therefore we can conclude that if we choose the second game then wining probability is greater than the first game.

That is why we should choose the second game.