How would you find the probability of drawing a face card and a 4 out of a standard deck of 52 cards? I got 4/13 but I don't think its right.
Anonymous -- I think you forgot the 4.
Theres 12 face cards (4 queens, 4 kings, and 4 jacks) and 4 fours. What would you do with 12/52 and 4/52?
oops. Guess I didn't read it right. Good catch.
Do I add them and that's it or do I do something else?
Jane, from your wording it is not clear if the first card drawn is returned to the deck or not.
Suppose it is not returned
could be F4 or 4F
= (12/52)(4/40) + (4/52)(12/40)
= 3/130 + 3/130
= 3/65
Your answer suggests that the card is returned after it is drawn.
Then it would be (12/52)(4/52) = 3/169 for the F4
but it could have been 4F, for another 3/169
so the prob when the card is returned = 3/169+3/169 = 6/169
To find the probability of drawing a face card (King, Queen, or Jack) and a 4 from a standard deck of 52 cards, we need to consider two events: drawing a face card and drawing a 4.
First, let's calculate the probability of drawing a face card. In a standard deck, there are 12 face cards (4 Kings, 4 Queens, and 4 Jacks) out of a total of 52 cards. So, the probability of drawing a face card is 12/52, which can be simplified to 3/13.
Next, let's calculate the probability of drawing a 4. In a standard deck, there are 4 cards with the value 4 (4 of Diamonds, 4 of Hearts, 4 of Clubs, and 4 of Spades) out of a total of 52 cards. So, the probability of drawing a 4 is 4/52, which can be simplified to 1/13.
To find the probability of both events occurring together (finding the probability of drawing both a face card and a 4), we multiply the probabilities of the two individual events. Therefore, the probability of both events happening together is (3/13) * (1/13) = 3/169.
So, the correct probability of drawing a face card and a 4 from a standard deck of 52 cards is 3/169, not 4/13.