Question

If you select one card at random from a standard deck of 52 cards, what is the probability that the card is black OR a 6?

Answer 1

Since there are 52 cards in the standard deck

Since half of them are in black

Then the probability of getting a black card is

`\begin{gathered} P(b)=((52)/(2))/(52) \\ P(b)=(26)/(52) \end{gathered}`

Since there are 4 cards of 6, then

The probability of getting 6 is

`P(6)=(4)/(52)`

OR in probability means adding, then

The probability of getting a black card or a 6 is

`\begin{gathered} P(b\text{ or 6)=}(26)/(52)+(4)/(52) \\ P(b\text{ or 6) =}(30)/(52) \end{gathered}`

We can simplify it by dividing up and down by 2

`\begin{gathered} P(b\text{ or 6)=}((30)/(2))/((52)/(2)) \\ P(b\text{ or 6)=}(15)/(26) \end{gathered}`

The answer is P(b or 6) = 30/52 OR 15/26