Question

Esmerelda flips a coin anddraws a card. What is theprobability that she gets"heads” and a black card?

Answer 1

For this problem we have two events given the first one is get a head (H) for the coin and a black card (B).

Let's find the probability for the event H. In a fair coin we can find the probability of obtain heads:

$P(H)=\frac{Possible\text{ cases}}{total\text{ cases}}=\frac{1}{2}$

Now let's find the probability of obtain a black card. In a standard deck we have 52 cards, 26 red and 26 black. So then the probability of obtain a black card is:

$P(B)=\frac{26}{52}=\frac{1}{2}$

Since we want the probability that she gets"heads” and a black card we can use the following rule assuming independence between the events:

$P(H\cap B)=P(H)\cdot P(B)=\frac{1}{2}\cdot\frac{1}{2}=\frac{1}{4}$