Question

Two cards are selected from a standard deck of 52 playing cards. The first card is not replaced before the second card is selected. Find the probability of selecting a four and then selecting a ten.

The probability of selecting four and then selecting a ten is ___? ​(Round to four decimal places as​ needed.)

Answer 1

P(Second card is ten and first card is four) = P(first card is four)*P(second card is ten | first card is four)

[Using the formula : ]

First draw

There are 52 cards in the deck out of which 4 cards are of number four. Thus, probability of selecting a four on the first draw:

P(four on first draw) = (No. of favourable outcomes)/(Total no. of outcomes) = 4/52 = 1/13

Second draw

After the first card showing four has been drawn there are 51 cards left out of which 4 are of number ten.

P(second card is ten | first card is four) = 4/51

Thus, P(Second card is ten and first card is four) = (1/13)*(4/51) = 4/663 = 0.0060

For any queries feel free to comment and ask.

If the solution was helpful to you, don't forget to upvote it by clicking on the 'thumbs up' button.