Question

You are playing a game of blackjack, and you want to know: what is the probability of being dealt a face card AND then an Ace to start the game?

Answer 1

a The total number of the card in a pack of card = 52

`\text{Total sample space= 52}`

The number of face card in a pack of cards is = 12

`\begin{gathered} \text{the picture cards are} \\ 4\text{ jacks+4 queens+4kings=12 picture cards} \end{gathered}`

The probability of getting a picture card will be

`\begin{gathered} Pr(\text{face card)=}\frac{Number\text{ of face cards}}{total\text{ sample space}} \\ Pr(face\text{ card)=}(12)/(52) \end{gathered}`

The number of ace card in a pack of cards = 4

Therefore,

The probability of picking an ace card will be

`\begin{gathered} Pr(\text{ace card)=}\frac{Number\text{ of ace cards}}{total\text{ sample space}} \\ Pr(\text{ ace card)=}(4)/(52) \end{gathered}`

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

`\begin{gathered} Pr(\text{face card)}* Pr(ace\text{ card)} \\ =(12)/(52)*(3)/(52) \\ =(3)/(169) \\ =(3)/(169)*100=1.7\text{ \%} \end{gathered}`

Therefore ,

The probability will be 3/169 or 1.7%

The right option will be OPTION D