Question

Maria is working on her card tricks and is having john draw cards so she can practice. what is the probability that john drew the 3 of hearts, replaced it, and then drew the 9 of spades?

Answer 1

Odds of 1-in-2,704 trials.

Or a 0.0369% probability.

Explanation:

Break it down:

What's the probability that a single specific card is drawn?

You have to know how many cards there are.

There are 52 cards in a deck, right?

So there's a 1-in-52 chance that a specific card will be drawn.

Make sense?

So there's a 1-in-52 (or 1/52, or 0.0192 [which is a 1.92%]) chance that the 3 of hearts (3H) will be drawn.

Or that any other designated card will be drawn.

(As long as there are still 52 cards to choose from, and we're told that the 3H is put back.)

So to find the probability that THIS particular card is drawn, followed by THAT particular card, you need to multiply the two probabilities:

1/52 x 1/52 = 1/2,704 chance

Or using decimals:

0.0192 x 0.0192 = 0.000369 chance

(Notice that dividing 1 by 2,704 gives the same answer.)

Convert that to percentage by dividing by 100 (which is just moving the decimal point two places to the right) to get a 0.0369% probability of drawing any two specified cards in sequence.

(Bonus problem: what if John doesn't put the first card back? Hint: how many cards are left to choose from if the 3H is removed?)