Question

Find probability of getting a queen or a diamond from a deck of cards

Answer 1

The probability of getting a queen or a diamond is the sum of the probabilities of getting a queen and getting a diamond, subtracting the probability of getting a queen of diamonds(so we don't count it twice).

In a deck of cards we have 52 cards(13 of each suit). The probability of getting a queen is the amount of queens in the deck(4) divided by the total amount of cards(52).

`P_Q=(4)/(52)`

The probability of getting a diamond, is the amount of diamond cards(13) divided by the total amount of cards(52).

`P_D=(13)/(52)`

And finally, the probability of getting a queen of diamonds is

`P_(QD)=(1)/(52)`

Now, we just need to add the probabilities of getting a queen and getting a diamond, and subtract the probability of getting a queen of diamonds.

`P(QorD)=P_Q+P_D-P_(QD)=(4)/(52)+(13)/(52)-(1)/(52)=(16)/(52)=(4)/(13)`

The probability of getting a queen or a diamond from a deck of cards is 4/13.