Afair die will be rolled 11 times. what is the probability that an odd number is rolled exactly 7 times?

0.161

Step-by-step explanation:

Given:

Number of trials,

Consider the event of rolling odd number as success. There are 3 odd and 3 even numbers in a fair die.

So, probability of success,

Probability of failure,

Number of successes,  

From Bernoulli's Theorem, the probability of successes in trials is given as,

Here,

So,

Therefore, the probability of getting an odd number exactly 7 times is 0.161.

(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

a triangular prism is a 3 dimensional shape composed of triangles and rectangles. it is made from two triangular bases and three rectangular sides.