Question

Twocardsaredrawnwithoutreplacement.Findtheprobabilitythat:a) Botharered.b) Botharethesamecolor.c) Firstcard is aface,secondcard is black.

Answer 1

`The\text{ probability that both selected cards are red is }(25)/(102)`

Here, we shall be considering a deck of cards

In a deck of cards, there are 52 cards, with 26 cards being red and the remaining 26 being black

When we draw cards without replacement, we are simply talking about taking the card and not returning it into the deck

So the probability of selecting a first red card will be;

number of red cards/number of cards in the deck

Mathematically, that would be 26/52 = 1/2

Now since we have taken the card, and we are not replacing it, the number of remaining red cards will be 25 while the number of the remaining total cards will be 51

The probability in this case will be ;

number of remaining red cards/number of remaining total cards = 25/51

So the probability of both being red is simply the product of both probabilities

That would be;

`(1)/(2)\text{ }*\text{ }(25)/(51)\text{ = }(25)/(102)`