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KATRIN_1 [288]
3 years ago
14

If P(A) = 0.25, P(B) = 0.60 and P(A and B) = 0.15, are the event A and B independent? Explain/show work.

Mathematics
1 answer:
babymother [125]3 years ago
7 0

Answer:

event A and B are independent because  P(A and B)  = P(A) x P(B) = 0.15

Step-by-step explanation:

When two events are independent, the probability of both occurring is the product of their separate probabilities, as expressed below;

P(A and B)  = P(A) x P(B)

Given;

P(A) =  0.25

P(B) = 0.60

P(A and B) = 0.15

Now, let's check if  P(A and B) will be equal to P(A) x P(B)

P(A) x P(B) =  0.25 x 0.60 = 0.15

P(A and B)  = P(A) x P(B), thus event A and B are independent.

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A company boss is planning on ordering a gift for each of his employees. He takes a sample of 30 employees in the company and as
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Answer:

I think the answer is 33

Step-by-step explanation:

Extremely sorry if it's wrong

6 0
1 year ago
in a school gym, the ratio of the number of boys to the number of girls was 4:3 . after 160 boys left the gym, the ratio became
Annette [7]

Answer:

300 girls were there in the gym.

Step-by-step explanation:

Given:

The ratio of the number of boys to the number of girls was 4:3, after 160 boys left the gym, the ratio became 4:5.

Now, to find the number of girls in the gym.

The girls in the gym does not left, their quantity is same before and after.

So, we multiply the both ratios to make the girls ratio same:

4:3 × 5 = 20:15

4:5 × 3 = 12:15

Now, <em>we find the units of the ratio</em>.

<em>The ratio of boys dropped down by 160</em>:

20 - 12 = 8 units.

160 = 8 units

Now, dividing both sides by 8 we get:

20 = 1 unit

So, 1 unit = 20.

Now, girls = 15 units

So, 15 × 20 = 300.

Therefore, 300 girls were there in the gym.

3 0
3 years ago
The angle of elevation from Madison to the top of the Statue of Liberty is 79 degrees. If Madison is standing 58.2 feet from its
lana66690 [7]
To solve this problem you must apply the proccedure shown below:

 1. You have the following information given in the problem:

 - <span>The angle of elevation from Madison to the top of the Statue of Liberty is 79 degrees.
 - Madison is standing 58.2 feet from its base.

 -Madison is 5 feet tall.

 2. Therefore, you have:

 Sin</span>α=opposite/hypotenuse
<span>
 Sin(79°)=x/58.2
 x=(58.2)(Sin(79°))
 x=57.13 ft

 3. Now, you can calculate the height of the Statue of Liberty, as below:

 height=x+5 ft
 height=57.13 ft+5 ft
 height=62.13 ft

 4. Therefore, as you can see, the answer is: 62.13 ft
</span>
4 0
3 years ago
Read 2 more answers
Simplify the expression.<br> 0.24 – 1.6
lukranit [14]

Answer:

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
A bakery has the following pricing for large orders of cupcakes. The first 100 cupcakes of any order
Taya2010 [7]

A piecewise function is a function that behaves differently in different intervals of its domain.

The answers are:

a)

f(x) = x*$2.00    if 0 ≤ x ≤ 100

f(x) = x*$1.75     if  100 < x ≤ 250

f(x) = x*$1.25     if    x > 250.

b)  $306.25

The given information is:

The first 100 cupcakes cost $2.00 each.

If the order is between 100 and 250 cupcakes, the cost is $1.75 each.

If the order is more than 250 cupcakes, the cost is $1.25 each.

a) Now we want to write the piecewise function, this will be:

f(x) = x*$2.00    if 0 ≤ x ≤ 100

f(x) = x*$1.75     if  100 < x ≤ 250

f(x) = x*$1.25     if    x > 250.

Above you can see the piecewise function, when you want to evaluate it, the first thing you need to do is to find at which interval the input belongs.

b) If you order 175 cupcakes you have x = 175.

This belongs to the second interval ( 100 < x ≤ 250) then we will use the second part of the function:

f(175) = 175*$1.75 = $306.25

If you want to learn more, you can read:

brainly.com/question/12561612

8 0
2 years ago
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