Question 1194403: Hello All! Would really appreciate your help with this question.
You have a standard deck of 52 cards. Find the probability of drawing an ODD card,then drawing a FACE card (without replacement)
(if you could please include an explanation, it will be very helpful - Thank you in advance)
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
The cards with numbers on them are: {2, 3, 4, 5, 6, 7, 8, 9, 10}
Some people would consider aces to be treated as 1 or 11, depending on the situation.
That would seem to point to aces being treated as an odd number.
However, I'll only consider cards that have actual numbers written on them.
In that set above, we have the following odd numbers: {3, 5, 7, 9}
There are four odd numbers listed, and four suits, giving 4*4 = 16 cards with an odd number on them.
The probability of picking an odd card is 16/52 = (4*4)/(4*13) = 4/13.
Let A = 4/13 so we can use it later.
We're told that the first card is not put back due to the "without replacement" key phrase. So we go from 52 cards to 52-1 = 51 cards total.
The number of face cards does not go down because we haven't picked any yet.
The face cards are: {Jack, Queen, King}
We have four suits, so there are 3*4 = 12 face cards.
The probability of a face card, after the first odd number card is not put back, is 12/51 = (4*3)/(17*3) = 4/17
Let B = 4/17
Multiply the values of A and B to get the probability of drawing an odd card, followed by a face card, with no replacement.
A*B = (4/13)*(4/17) = (4*4)/(13*17) = 16/221 is the final answer.
If you need the result as a decimal, then it is approximately 16/221 = 0.0724 which converts to 7.24%
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