Archive for November, 2015

Problem 1174

If there are where multiple-choice questions on an exam, each having four possible answers, how many different sequences of answers are there?

 

Solution:-

 

If any one of k different mutually exclusive and collectively exhaustive events can occur on each of n trials, the number of possible outcomes is equal to kn.

The four possible answers to each multiple-choice question are mutually exclusive and collectively exhaustive. There are twelve questions.

K = 4 and n = 12

Substitute 4 for k and 12 for n in the expression kn and simplify.

kn = 412

=16777216

There are 16777216 different square of answers.

 

Problem 1172

Complete the sentence below.

If the radius of a circle is r and the length if the arc subtended by a center angle is also r, then the measure of the angle is 1________?

 

Solution:-

 

radian.

 

Problem 1171

Complete the sentence below.

An angle θ is in ____________if its vertex is at the origin of a rectangular coordinate system and its initial side coincides with the positive x-axis.

 

Solution:-

 

Standard position

 

Problem 1170

Complete the following sentence.

If a particle has a speed of r feet per second and travels a distance d (in feet) in time (in seconds), then

d = ______________.

Solution:-

 

d = r*t

 

Problem 1169

What is the formula for the circumference C of a circle of radius r? What is the formula for area A of a circle of a radius r?

 

Solution:-

 

The formula for the circumference C of a circle of radius r is C = 2πr.

The formula for the area A of a circle of radius r is A = πr2.

 

Problem 1168

Find P(B∩E) directly from the table.

  A B C Total
D 0.13 0.02 0.05 0.20
E 0.37 0.28 0.15 0.80
Total 0.50 0.30 0.20 1.00

 

Solution:-

 

If F and G are two events in sample space S, than the union of F and G, denoted by FUG, is define to be FUG = {e ϵS | e ϵ F or e ϵ G}, and the intersection of F and G, denoted by F∩G, is defined to be F∩G = {e ϵS | e ϵ F or e ϵ G}. Furthermore, FUG is also define to be the event F or G, while F∩G is also define to be the event F and G.

The event B∩E is define to be the event B and E.

The value of P(B∩E) can be found where the column containing B and the row containing E intersect.

Find P(B∩E) directly from the table.

P(B∩E) = 0.28

 

 

Problem 1167

A pair dice is rolled. What is the probability of getting a sum of 8?

 

Solution:-

 

To find the probability of an event, denoted P(E), you need to find the number of possible outcomes of the experiment, n(s) . This is the same as the number if elements in the sample space. You also need to find the number of ways the event can occur, denoted n(E).

Then use the formula p(E) = \frac{n(E)}{n(S)}.

The experiment in this case is the rolling of two dice.

Sum= 8({2,6},{3,5},{4,4},{5,3},{6,2})

By counting all possible outcomes it is clear that n(s) = 36.

For the event of getting a sum of 8, the number of possible outcomes is 5.

Thus n(E) = 5.

Therefore, P(E) = \frac{n(E)}{(S)} = \frac{5}{36}.

 

Problem 1166

If the probability is 0.81 that a candidate wins the election, what is the probability that he loss?

 

Solution:-

 

Suppose that we divide a final sample space into two sunset E and E’ such that E∩E’ = ø, that is they are mutually exclusive, and EUE’ = S. Then E’ called the complement of E relative to S. Thus, E’ contains all the elements of S that are not in E.

Because the events are mutually exclusive, P(E’) = 1- P(E).

Let E = the candidate wins and let E’ = the candidate, use P(E’) = 1 –P(E) to find the probability that the candidate loses the election.

Substitute P(E) into the equation below.

P(E’) = 1-0.81

Calculate P(E’)

P(E’) = 0.19

Therefore, the probability that the candidate loses the election is 0.19.

 

Problem 1165

A single card is drawn from a standard 52-cards deck. Let R be the event that the card drawn is red, and let F be the event that the card drawn is a face card. Find the indicated probability.
P(R’ U F)
Solution:-

 

P(R’ U F) = \frac{8}{13}

 

 

Problem 1164

Is the selection a permutation, a combination, or neither?

A group of 10 friends sits in the same row in a movie theater.

 

Solution:-

 

Use the definition of permutation and combination to determine the type of selection mode.

A permutation of a set of n distinct objects is an arrangement of the objects in a specific order without repetition.

A combination of a set of n distinct objects in an arrangement of the objects without repetition where order is irrelevant.

In the selection process of the problem, the order in which the friends sit is important.

There will not be any repetition since a person cannot sir in multiple seats at the same time.

Use the fact that the selection process has no repetition and order is relevant to determine the type of selection.

The selection is a permutation.