Question

It was shown that in a 52-card deck, any given card has a 1/ 52 = 0,02 chance of being selected in a random draw. How would this probability change after a card was drawn and not replaced? Calculate the successive changes in probability as one, two, three, four, and five cards are taken from the deck. Does the probability for each remaining card increase or decrease? Why?

Answer 1

When none of the card is selected

then probability of randomly selecting any one card is 1/52 = 0.01923

Now, one card is selected and we have only 51 cards left

so, probability of randomly selecting second card is favorable/total

= 1/51 = 0.01961

Now, 2 cards are selected and we have only 50 cards left

so, probability of randomly selecting third card is favorable/total

= 1/50 = 0.02000

Now, 3 cards are selected and we have only 49 cards left

so, probability of randomly selecting fourth card is favorable/total

= 1/49 = 0.02041

Now, 4 cards are selected and we have only 48 cards left

so, probability of randomly selecting fifth card is favorable/total

= 1/48 = 0.02083

We can see that the probability is increasing because the number of total outcome is decreasing(52 then 51 then 50, and so on), but favorable outcome remains same, i.e. 1