Answer:
a) 13/51
b) 1/4
Explanation:
the first thing to note is that probability is the (number of favorable outcomes)/(number of outcomes). for example, to find the probability we get a black card is (number of black cards)/(number of total cards)
a) without replacement means we don't put the card back into the deck. a deck has 26 red cards and 26 black cards, out of 52 in total
the first card has to be black, so the probability that the first card is black is 26/52, and this simplifies to 1/2.
next, we have 26 red cards, 25 black cards and 51 total cards since we remove that black card.
the probability that we get a red card is 26/51.
so, we multiply the probabilities together:
1/2 × 26/51 = 26/(2×51) this simplifies to 13/51.
b) now with replacement we have to put the card back. again, we have the probability of getting a black card as the first is 26/52 or 1/2.
then, we place the card back so we have 26 red cards, 26 black cards and 52 total again.
probability of getting a red card is 26/52 as well, or 1/2.
so, our total probability is the product of these:
1/2 × 1/2 = 1/4.