On a standard 52 card deck, calculate the probability.

that on card is either a queen or a heart

draw one card, what is the probability that it is a king, given that it is a club?

Thanks

The first one is to draw one card that is either a queen and a heart

thanks

It would help if you proofread your questions before you posted them.

It is "either a queen or a heart" or "both a queen and a heart."

To calculate the probability, we first need to determine the total number of favorable outcomes and the total number of possible outcomes.

1. Probability of drawing either a queen or a heart:
- There are four queens in a deck (one for each suit: hearts, diamonds, clubs, spades).
- There are 13 hearts in a deck (one for each rank: Ace, 2, 3, ..., 10, Jack, Queen, King).
- However, we have counted the Queen of Hearts twice (as both a queen and a heart). So, we subtract one.
- Therefore, the number of favorable outcomes is 4 queens + 13 hearts - 1 Queen of Hearts = 16.
- The total number of possible outcomes is 52, which is the total number of cards in a deck.
- So, the probability of drawing either a queen or a heart is 16/52 = 4/13.

2. Probability of drawing a king, given that it is a club:
- There are four kings in a deck (one for each suit).
- There are 13 clubs in a deck (one for each rank).
- Therefore, the number of favorable outcomes is 4 (the number of kings).
- The total number of possible outcomes is 13 (the number of clubs).
- So, the probability of drawing a king, given that it is a club, is 4/13.

I hope this helps! Let me know if you have any further questions.

Does the first mean that it cannot be a queen and a heart? If so,

3/52 + 13/52 or 4/52 + 12/52 = 16/52 = 4/13

King of clubs = 1/52