A card is drawn from a well shuffled pack of playing cards. Find the probability that it is either black or queen?

Sure, let's solve this step by step.

Step 1: Understand the problem We have a standard deck of 52 playing cards. There are 26 black cards (clubs and spades) and 4 queens in the deck. We need to find the probability that the card drawn is either black or a queen.

Step 2: Define the events Let's define: Event A: drawing a black card Event B: drawing a queen

Step 3: Calculate the probabilities of the events The probability of event A, P(A), is the number of black cards divided by the total number of cards, so P(A) = 26/52 = 1/2. The probability of event B, P(B), is the number of queens divided by the total number of cards, so P(B) = 4/52 = 1/13.

Step 4: Calculate the probability of the intersection of the events The intersection of events A and B is drawing a black queen. There are 2 black queens in the deck, so the probability of this, P(A ∩ B), is 2/52 = 1/26.

Step 5: Use the formula for the probability of the union of two events The probability that either event A or event B occurs, P(A ∪ B), is given by the formula P(A ∪ B) = P(A) + P(B) - P(A ∩ B).

Step 6: Substitute the values into the formula P(A ∪ B) = 1/2 + 1/13 - 1/26 = 26/52 + 4/52 - 2/52 = 28/52 = 7/13.

So, the probability that the card drawn is either black or a queen is 7/13.