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Sagot :
We have to calculate the probability of picking a 4 and then a 5 without replacement.
We can express this as the product of the probabilities of two events:
• The probability of picking a 4
,• The probability of picking a 5, given that a 4 has been retired from the deck.
We have one card in the deck out of fouor cards that is a "4".
Then, the probability of picking a "4" will be:
[tex]P(4)=\frac{1}{4}[/tex]The probability of picking a "5" will be now equal to one card (the number of 5's in the deck) divided by the number of remaining cards (3 cards):
[tex]P(5|4)=\frac{1}{3}[/tex]We then calculate the probabilities of this two events happening in sequence as:
[tex]\begin{gathered} P(4,5)=P(4)\cdot P(5|4) \\ P(4,5)=\frac{1}{4}\cdot\frac{1}{3}=\frac{1}{12} \end{gathered}[/tex]Answer: 1/12
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