70.1k views
5 votes
Use the formula for the probability of the complement of an event.A single card is drawn from a deck. What is the probability of not drawing a 7?

User Rokin
by
8.2k points

1 Answer

0 votes

occur

the answer is 12/13 or 0.932

Step-by-step explanation

when you have an event A, the complement of A, denoted by.


A^(-1)

consists of all the outcomes in wich the event A does NOT ocurr

it is given by:


P(A^(-1))=1-P(A)

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


P=\frac{favorable\text{ outcomes}}{\text{total outcomes}}

so

let

favorable outcome = 4 (there are four 7 in the deck)

total outcomes=52

hence,replacing


\begin{gathered} P=(4)/(52)=(1)/(13) \\ P(A)=(1)/(13) \end{gathered}

Step 2

now, to find the probability that the event does NOT ocurrs ( not drawing a 7)

let's apply the formula


P(A^(-1))=1-P(A)

replace


\begin{gathered} P(A^(-1))=1-(1)/(13) \\ P(A^(-1))=(13-1)/(13)=(12)/(13) \\ P(A^(-1))=0.923 \end{gathered}

therefore, the answer is 12/13 or 0.932

I hope this helps you

User Kike Gamboa
by
8.6k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.