occur
the answer is 12/13 or 0.932
Explanation
when you have an event A, the complement of A, denoted by.
[tex]A^{-1}[/tex]consists of all the outcomes in wich the event A does NOT ocurr
it is given by:
[tex]P(A^{-1})=1-P(A)[/tex]Step 1
find the probability of event A :(P(A)
The probability of an event is the number of favorable outcomes divided by the total number of outcomes possible
[tex]P=\frac{favorable\text{ outcomes}}{\text{total outcomes}}[/tex]so
let
favorable outcome = 4 (there are four 7 in the deck)
total outcomes=52
hence,replacing
[tex]\begin{gathered} P=\frac{4}{52}=\frac{1}{13} \\ P(A)=\frac{1}{13} \end{gathered}[/tex]Step 2
now, to find the probability that the event does NOT ocurrs ( not drawing a 7)
let's apply the formula
[tex]P(A^{-1})=1-P(A)[/tex]replace
[tex]\begin{gathered} P(A^{-1})=1-\frac{1}{13} \\ P(A^{-1})=\frac{13-1}{13}=\frac{12}{13} \\ P(A^{-1})=0.923 \end{gathered}[/tex]therefore, the answer is 12/13 or 0.932
I hope this helps you
