Respuesta :
a The total number of the card in a pack of card = 52
[tex]\text{Total sample space= 52}[/tex]The number of face card in a pack of cards is = 12
[tex]\begin{gathered} \text{the picture cards are} \\ 4\text{ jacks+4 queens+4kings=12 picture cards} \end{gathered}[/tex]The probability of getting a picture card will be
[tex]\begin{gathered} Pr(\text{face card)=}\frac{Number\text{ of face cards}}{total\text{ sample space}} \\ Pr(face\text{ card)=}\frac{12}{52} \end{gathered}[/tex]The number of ace card in a pack of cards = 4
Therefore,
The probability of picking an ace card will be
[tex]\begin{gathered} Pr(\text{ace card)=}\frac{Number\text{ of ace cards}}{total\text{ sample space}} \\ Pr(\text{ ace card)=}\frac{4}{52} \end{gathered}[/tex]In probability, when the word AND is used we will have to use the multiplication sign(×)
Therefore, the probability of dealing with a face card and an ace card will be
[tex]\begin{gathered} Pr(\text{face card)}\times Pr(ace\text{ card)} \\ =\frac{12}{52}\times\frac{3}{52} \\ =\frac{3}{169} \\ =\frac{3}{169}\times100=1.7\text{ \%} \end{gathered}[/tex]Therefore ,
The probability will be 3/169 or 1.7%
The right option will be OPTION D
