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Assume that we have two events, and , that are mutually exclusive. Assume further that we know and . If an amount is zero, enter

sweet [91]

Answer:

Explained below.

Step-by-step explanation:

The complete question is:

Assume that we have two events, A and B, that are mutually exclusive. Assume further that we know P(A) = 0.30 and P(B) =0.40.

What is P(A and B)?

What is P(A | B)?

Is P(A | B) equal to P(A)?

Are events A and B dependent or independent?

A student in statistics argues that the concepts of mutually exclusive events and independent events are really the same, and that if events are mutually exclusive they must be independent. Is this statement accurate?

What general conclusion would you make about mutually exclusive and independent events given the results of this problem?

Solution:

The probability of the two events A and B are:

P(A) = 0.30 and P(B) =0.40

(a)

Compute the value of P (A ∩ B) as follows:

$P(A\cap B)=0$

This is because mutually exclusive events are those events that cannot occur together.

(b)

Compute the value of P (A | B) as follows:

$P(A|B)=\frac{P(A\cap B)}{P(B)}=\frac{0}{0.40}=0$

Thus, the value of P (A | B) is 0.

(c)

No, P (A | B) is not equal to the P (A).

(d)

As mentioned in part (a), mutually exclusive events are those events which cannot occur together.

That is, $P(A\cap B)=0$ .

Events A and B are independent if the chance of their concurrent happening is equivalent to the multiplication of their distinct probabilities.

That is, $P(A\cap B)=P(A)\times P(B)$ .

The concepts of mutually exclusive events and independent events are not the same.

(e)

As the it is provided that A and B are mutually exclusive events, we know that $P(A\cap B)=0$ .

Now compute the value of $P(A)\times P(B)$ as follows:

$P(A)\times P(B)=0.30\times 0.40=0.12\neq 0$

Thus, the events A and B are not independent.

Thus, if two events are mutually exclusive events they cannot be independent.

4 0

3 years ago

The sine ratio of an angle is the opposite side over the adjacent side.

Agata [3.3K]

Answer:

never

Step-by-step explanation:

In a right triangle, every angle has an opposite side and an adjacent side. And there's always a hypotenuse.

The sine of an angle is the ratio of the length of the opposite side divided by the length of the hypotenuse.

The tangent ratio of an angle is the opposite side over adjacent side, it is not the sine ratio of a triangle.

For example, ABC is a right angled triangle having length of the sides are a,b,c.

So

$sine\ C=\frac{a}{c}$

3 0

2 years ago

Mr. Young is offered an investment opportunity. Kyra says she will invest his money at a 6% simple interest rate over the next 7

gregori [183]

Answer:

$126

Step-by-step explanation:

Given that:

Investment is done as per Simple interest.

Principal = $3000

Time for which the investment is to done = 7 years

Rate of interest = 6%

To find:

Interest earned when the investment matures?

Solution:

Formula for Simple Interest :

$Simple\ Interest = \dfrac{PRT}{100}$

Where $P$ is the principal amount

$R$ is the Rate of Interest

$T$ is the time for which the investment is made

Putting the given values:

$Simple\ Interest = \dfrac{3000\times 6\times 7}{100}\\\Rightarrow Simple\ Interest = \dfrac{12600}{100}\\Simple\ Interest = \$126$

Therefore, the answer is:

Interest earned is $126.

8 0

2 years ago

A rectangular prism is 20 meters long, 13 meters wide, and 5 meters high. What is the surface area of the rectangular prism?

RUDIKE [14]

Answer:

850m^2

Step-by-step explanation:

Look at the formula SA=L*W*H. And plug in the numbers pertaining the question! hints on to what to add is stuff like "long" for length, "wide" for width, and "high" for height! And use a calculator, or scetch it out to find your total answer!

Hope this helps!

3 0

2 years ago

In the Central City Grand Prix, out of 30 cars that started the race, 12 of them finished. What percent of the cars finished the

snow_lady [41]

To get the answer we can use proportion.
30----------100%
12-----------x
Cross multiply now
30x=12*100%
30x=1200% /:30 (divide both sides by 30)
x=40% - it's the percentage of cars which finished the race.
100%-40%=60% - it's the answer

3 0

2 years ago