Asingle card is drawn from a deck. find the probability of selecting a heart or a 8.

Answer with Step-by-step explanation:

Let

A:selecting a heart

Total cards=52

number of hearts=13

P(A)=13/52

B:selecting a 8

number of 8=4

P(B)=4/52

A∩B:selecting a heart with 8 on it

number of hearts with 8 on it=1

P(A∩B)=1/52

A∪B:selecting a heart or a 8

We have to find P(A∪B)

P(A∪B)=P(A)+P(B)-P(A∩B)

          =

          =

          = 16/52

          = 4/13

Hence, the probability of selecting a heart or a 8 is:

4/13

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3