Find the indicated probability. Round to the nearest thousandth. A study conducted at a certain college shows that 55% of the school's graduates find a job in their chosen field within a year after graduation. Find
the probability that among 7 randomly selected graduates, at least one finds a job in his or her chosen field within a year of graduating.
0.985
0.996
0.550
0.143

Step-by-step explanation:

Given

Proportion = 55%

Required

Probability that at least one out of 7 selected finds a job

Let the proportion of students that finds job be represented with p

Convert to decimal

Let the proportion of students that do not find job be represented with q

Such that;

Make q the subject of formula

In probability; opposite probabilities add up to 1;

In this case;

Probability of none getting a job + Probability of at least 1 getting a job = 1

Represent Probability of none getting a job with P(none)

Represent Probability of at least 1 getting a job with P(At least 1)

So;

Solving for the probability of none getting a job using binomial expansion

Where and n = 7; i.e. total number of graduates

For none to get a job, means 0 graduate got a job;

So, we set r to 0 (r = 0)

The probability becomes

Substitute 7 for n

Substitute and

Recall that

Substitute

Make P(At least 1) the subject of formula

(Approximated)

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it