Question

two cards are selected from a standard deck of 52 cards the first is not replacedbefore the secondcards is selected Find the probability of selecting a five and then selectinga a jack

Answer 1

The probability of finding a five in the first draw, is the amount of '5' inside the deck(4) divided by the total amount of cards in the deck(52).

`p_1=(4)/(52)`

The probability of drawing a jack follows the same logic, but since this is the second draw and the cards are not replaced, the total amount of cards decreases by one. We have 4 jacks and 51 cards.

`p_2=(4)/(51)`

Since each draw is an independent event, the probability of both things happening at the same time is given by the product of the probabilities of each individual draw.

`p_1* p_2=(4)/(52)*(4)/(51)=(16)/(2652)=(4)/(663)=0.0060331825\ldots`

The probability of drawing a five and then drawing a jack is around 0.6%.