Question

Given the following cards, what is the probability of drawing a blue card, not replacing it, and then drawing another blue card?

Answer 1

There are 5 cards total, "sample space of 5", there are 3 blue cards, "favorable outcomes of 3".

the chances of getting the first blue will be 3/5.

once the first blue is pulled out, and not put back, the sample spaced changed to 4, and since there are only 2 blue cards, the favorable outcomes changed to only 2.

the chances of getting the 2nd blue card is 2/4 or 1/2.

P( second blue | first blue) = P(first blue) * P(second blue)

$\bf \stackrel{first~blue}{\cfrac{3}{5}}\stackrel{AND}{\cdot} \stackrel{second~blue}{\cfrac{2}{4}}\implies \cfrac{3}{10}$