An interviewer is given a list of people she can interview. if the interviewer needs to interview 5 people, and if each person (independently) agrees to be interviewed with probability 2/3, what is the probability that her list of people will enable her to obtain her necessary number of interviews if the list consists of (a) 5 people and (b) 8 people? for part (b), what is the probability that the interviewer will speak to exactly (c) 6 people and (d) 7 people on the list?

a) 0.1317

b) 0.7413

c) 0.2731

d) 0.1561

Step-by-step explanation:

Let's start defining the random variable.

X : ''The number of people that she interviews''

X ~ Bi (n,p)

This means, X can be modeled as a Binomial random variable where p is the success probability and n is the number of independent Bernoulli experiments that take place. In this case, n is the number of interviews that she makes.

The probability function for X is :

Where nCx is the combinatorial number defines as :

For a)

We are looking for the probability of she interviews 5 people over 5 she interviews ⇒

b)  In this part , we are looking for P(X ≥ 5) when n = 8 (Number of people she interviews)

c)  Interview 6 people of 8 :

d) Interview 7 people of 8 :

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

the ratio of white tiles to blue tiles is 48: 16. the ratio in it's simplest form is 3: 1.

step-by-step explanation:

ratio: take the first number and add a colon next to it, then add the second number after that. make sure the ratio order matches up with the written problem!

simplest form: we can simplify the ratio 48 : 16 by dividing both terms by the greatest common factor (gcf).

the gcf of 48 and 16 is 16.

divide both terms by 16:

48 ÷ 16 = 3

16 ÷ 16 = 1

reducing to simplest form:

48 : 16 = 3 : 1