Question

There are five cards in front of you, in a random order face down; 10,J,Q,K, A. If you draw the 10, you will lose. You have to draw twice in a row,what are your chances of winning?

Answer 1

You have five cards in a random order face down.

{10, J, Q, K, A}

Assuming that the cards have the same probability of being chosen.

The probability of choosing a card at random at it being 10 can be calculated as the number of times 10 is on the deck by the total number of cards:

`P(10)=(1)/(5)`

And the probability of choosing a card at random an it "not being 10" can be calculated as the number of cards that are "not 10" by the total number of cards

that is:

`P(not10)=(4)/(5)`

If you choose two cards in a row, you will win if both times the card is "not 10", then you have to calculate that the first card is "not 10" and the second card is also "not 10"

`P(not10\cap not10)=P(not10)\cdot P(not10)=(4)/(5)\cdot(4)/(5)=(16)/(25)`

Expressed as a decimal value it is 0.64 and as a percentage 64%

So the probability of choosing two cards at random and not obtaining 10 is 64%