If a certain coin is flipped, the probability that the coin will land heads up is 1/2. if the coin is flipped 5 times, what is the probability that it will land heads up on the first 3 flips and not on the last 2 flips?
a) 3/5
b) 1/2
c) 1/5
d) 1/8
e) 1/32

Option: E is the correct answer.

      The probability is:

                E)  1/32

We know that the outcome on each of the 5 flips are independent of each other.

The probability that the coin will land heads up is 1/2.

The probability that the coin will not land on heads  is 1/2.

( Since,

1-(1/2)=1/2  )

Hence,  the probability that it will land heads up on the first 3 flips and not on the last 2 flips is:

Head on first×Head on second×Head on third×Tail on fourth×Tail on fifth

(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

the aswere is the one with all 8's and the second one is with the 10,8 and 6

step-by-step explanation: