Question

Imagine a deck of 500 cards numbered from 1 to 500. If all the cards are shuffled randomly and you are asked to pick three cards, one at a time, what's the probability of each subsequent card being larger than the previous drawn card

Answer 1

Answer:

P = 1 / 6

Step-by-step explanation:

Given:-

- A deck has 500 cards

- Numbered from 1-500

Find:-

you are asked to pick three cards, one at a time, what's the probability of each subsequent card being larger than the previous drawn card

Solution:-

- Suppose we draw three cards. We don't care what they actually are, irrespective of number.

- Let the three numbers be a, b, c: Such that:

                                       a < b < c.

- The total possible combinations with 3 numbered cards will be:

                                       a b c

                                       b a c

                                       a c b

                                       b a c

                                       b c a

                                       c a b

- We have 6 possibilities for 3 numbered cards. So the probability of  of each subsequent card being larger than the previous drawn card would be:

                                     P = 1 / possible combinations

                                    P = 1 / 6