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).

$P_Q=\frac{4}{52}$

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

$P_D=\frac{13}{52}$

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

$P_{QD}=\frac{1}{52}$

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.

$P(QorD)=P_Q+P_D-P_{QD}=\frac{4}{52}+\frac{13}{52}-\frac{1}{52}=\frac{16}{52}=\frac{4}{13}$

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