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}}=(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)=(26)/(52)=(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)=(1)/(2)\cdot(1)/(2)=(1)/(4)`