The total number of cards in a pack of cards is
[tex]=52[/tex]The number of face cards in a pack of cards is
[tex]=12[/tex]The probability of picking one face card is
[tex]Pr(\text{face card)=}\frac{\text{number of face card}}{\text{total number of cards}}[/tex][tex]Pr(\text{face card)=}\frac{12}{52}[/tex]Step 2: We are to pick a second card without replacement
The total number of cards will now be
[tex]=51[/tex]While the number of face cards will now be
[tex]=11[/tex]The probability of picking one face card is
[tex]Pr(\text{face card)=}\frac{\text{number of face card}}{\text{total number of cards}}[/tex][tex]Pr(2nd\text{Face card)=}\frac{11}{51}[/tex]Step 3: We are to calculate the probability of picking the third card without replacement
The probability of picking one face card is
[tex]Pr(\text{face card)=}\frac{\text{number of face card}}{\text{total number of cards}}[/tex]The total number of cards will now be
[tex]=50[/tex]While the number of face cards will now be
[tex]=10[/tex][tex]Pr(3rd\text{face card)}=\frac{10}{50}[/tex]Step 4: We will calculate the probability of picking the fourth face card
The total number of cards will now be
[tex]=49[/tex]While the number of face cards will now be
[tex]=9[/tex]The probability of picking one face card is
[tex]Pr(\text{face card)=}\frac{\text{number of face card}}{\text{total number of cards}}[/tex][tex]Pr(4th\text{face card)}=\frac{9}{49}[/tex]Therefore,
The probability of picking 4 face cards without replacement will be
[tex]\begin{gathered} =\frac{12}{52}\times\frac{11}{51}\times\frac{10}{50}\times\frac{9}{49} \\ =\frac{99}{54145} \\ =0.001828 \end{gathered}[/tex]Hence,
The final answer is= 0.001828
