Mr. Jones has insomnia once a week. If he had an insomnia, he will definitely drink a cup of coffee in the morning. If he got a good night sleep, he will drink coffee with probability 1/2. Let I be the event that he has insomnia. Let C be the event that he drinks coffee in the morning. Given the information above: P(I) = 1/7, P(C|I) = 1 and P(C|I) = 1/2.

Find probability that he drinks coffee in the morning.

Step-by-step explanation:

Given:

I is the event that he has insomnia.

C is the event that he drinks coffee in the morning.

We want to determine the probability that he drinks coffee in the morning, P(C).

Using the Law of Total Probability

The probability that he drinks coffee in the morning is

(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

2500

step-by-step explanation: