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vladimir2022 [97]
3 years ago
13

You have a standard deck of 52 cards. You pick one card from the deck and then, without putting the first one back, pick a secon

d card. What is the probability that both cards will be 9s?
Mathematics
1 answer:
Nina [5.8K]3 years ago
7 0
Set up the two events
A = first card is a 9
B = second card is a 9

The probability for event A is
P(A) = 4/52
because there are four "9" cards out of 52 total

If event A happens first, and B follows, then the probability is
P(B|A) = 3/51
because there are 3 nines left over out of 52-1 = 51 total left over
No replacement has been made
The notation P(B|A) means "probability of event B given that event A has happened"

Multiply the probabilities
P(A and B) = P(A)*P(B|A)
P(A and B) = (4/52)*(3/51)
P(A and B) = (4*3)/(52*51)
P(A and B) = 12/2652
P(A and B) = 1/221
P(A and B) = 0.00452488687782

Rounded to 4 decimal places, the approximate answer is 0.0045
The exact answer as a fraction is 1/221
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\huge\text{Hey there!}


\huge\textsf{Breaking the meaning down in simpler terms}
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\huge\textbf{Mean:}\\\large\text{is understood to be the \bf total.}

\huge\textsf{Formulas for each term}

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\huge\textbf{SOLVING FOR THE QUESTION}

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\huge\text{Good luck on your assignment \& enjoy your day!}

<h3>
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