Question

If you select one card at random from a standard deck of 52 cards, what is the probability of that card being a 4, 5 OR 6? State your answer as a fraction.

Answer 1

The probability of A or B when you have mutually exclusive events (ones that can't happen at the same time) is:

`P(\text{A or B)=P(A)+P(B)}`

Let's call A the probability of getting a 4, B the probability of getting a 5 and C the probability of getting a 6.

Then in the deck, there are 4 cards with the number 4, then the probability of A is:

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

There are 4 cards with the number 5, and 4 cards with the number 6, then the probabilities of B and C are:

`\begin{gathered} P(B)=(4)/(52) \\ P(C)=(4)/(52) \end{gathered}`

Thus, the probability of A or B or C is:

`\begin{gathered} P(A\text{ or B or C)=P(A)+P(B)+P(C)} \\ P(A\text{ or B or C)=}(4)/(52)+(4)/(52)+(4)/(52) \\ P(A\text{ or B or C)=}(4+4+4)/(52) \\ P(A\text{ or B or C)=}(12)/(52) \\ \text{ Simplify} \\ P(A\text{ or B or C)=}(3)/(13) \end{gathered}`

Answer: The probability of that card being a 4, 5 or 6 is 3/13