Question

you are dealt one card from a 52 - card deck. find the probability that you are not dealt a black picture card. click the icon to view a description of a standard deck of playing cards. the probability is (type an integer or a simplified fraction.)

Explanation:

Step1: Determine number of black picture cards

In a standard 52 - card deck, picture cards are Jacks, Queens, and Kings. There are 2 suits (Spades and Clubs) that are black, and 3 picture - card ranks in each suit. So the number of black picture cards is $2\times3 = 6$.

Step2: Calculate probability of getting a black picture card

The probability of getting a black picture card when drawing one card from a 52 - card deck is $P(\text{black picture})=\frac{6}{52}=\frac{3}{26}$.

Step3: Calculate probability of not getting a black picture card

The probability of an event $A$ not occurring is $P(\overline{A}) = 1 - P(A)$. So the probability of not getting a black picture card is $P(\text{not black picture})=1-\frac{3}{26}=\frac{26 - 3}{26}=\frac{23}{26}$.

Answer:

$\frac{23}{26}$