1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
igor_vitrenko [27]
2 years ago
8

If the probability that a chef likes carrots is 0.13, the probability of those who like broccoli is 0.72, and the probability of

those who like neither is 0.22, what is the probability of those who like both
Mathematics
1 answer:
rosijanka [135]2 years ago
6 0

Taking into account definition of probability, the probability of those who like both is 0.07 or 7%.

<h3>Definition of Probabitity</h3>

Probability is the greater or lesser possibility that a certain event will occur.

In other words, the probability is the possibility that a phenomenon or an event will happen, given certain circumstances. It is expressed as a percentage.

<h3>Union of events</h3>

The union of events, AUB, is the event formed by all the elements of A and B. That is, the event AUB is verified when one of the two, A or B, or both occurs. AUB is read as "A or B".

The probability of the union of two compatible events is calculated as the sum of their probabilities subtracting the probability of their intersection:

P(A∪B)= P(A) + P(B) -P(A∩B)

where the intersection of events, A∩B, is the event formed by all the elements that are, at the same time, from A and B. That is, the event A∩B is verified when A and B occur simultaneously.

<h3>Complementary event</h3>

A complementary event, also called an opposite event, is made up of the inverse of the results of another event. That is, That is, given an event A, a complementary event is verified as long as the event A is not verified.

The probability of occurrence of the complementary event A' will be 1 minus the probability of occurrence of A:

P(A´)= 1- P(A)

<h3>Events and probability in this case</h3>

In first place, let's define the following events:

  • C: The event that a chef likes carrots.
  • B: The event that a a chef likes broccoli.

Then you know:

  • P(C)= 0.13
  • P(B)= 0.72

In this case, considering the definition of union of events, the probability that a chef likes carrots and broccoli is calculated from:

P(C∪B)= P(C) + P(B) -P(C∩B)

Then, the probability that a chef likes carrots and broccoli is calculated as:

P(C∩B)= P(C) + P(B) -P(C∪B)

In this case, considering the definition of the complementary event and its probability, the probability that a chef likes NEITHER of carrots and broccoli is calculated as:

P [(C∪B)']= 1- P(C∪B)

In this case, the probability of those who like neither is 0.22

0.22= 1 - P(C∪B)

Solving

0.22 - 1= - P(C∪B)

-0.78= - P(C∪B)

- (-0.78)= P(C∪B)

<u><em>0.78= P(C∪B)</em></u>

Now, remembering that P(C∩B)= P(C) + P(B) -P(C∪B), you get:

P(C∩B)= 0.13 + 0.72 -0.78

Solving:

P(C∩B)= 0.07=  7%

Finally, the probability of those who like both is 0.07 or 7%.

Learn more about probability:

brainly.com/question/25839839

brainly.com/question/26038361

#SPJ1

You might be interested in
Tina's gross pay is $2680. How much of her gross pay will be deducted for FICA taxes?
Burka [1]
<span>2680 * 6.2% = $166 
Make sure you add the amount that is supposed to be deducted when you attempt to solve your problems, I'm a visual learner and I usually find it best to write everything out to see where to go next. <3 do well my dear</span>
3 0
3 years ago
Hello, I really struggle with math and I was wondering if you could help me with the following problem please? It will be much a
xz_007 [3.2K]

Answer:

x=7

Step-by-step explanation:

Simplifying

3x + 2(4 + 6x) = 113

3x + (4 * 2 + 6x * 2) = 113

3x + (8 + 12x) = 113

Reorder the terms:

8 + 3x + 12x = 113

Combine like terms: 3x + 12x = 15x

8 + 15x = 113

Solving

8 + 15x = 113

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-8' to each side of the equation.

8 + -8 + 15x = 113 + -8

Combine like terms: 8 + -8 = 0

0 + 15x = 113 + -8

15x = 113 + -8

Combine like terms: 113 + -8 = 105

15x = 105

Divide each side by '15'.

x = 7

Simplifying

x = 7

5 0
2 years ago
Read 2 more answers
Peter has a dozen sticks of butter.He needs 1/6 of a stick to make an omelet.How many omelets can peter make
PilotLPTM [1.2K]

Answer:

<em>72 omelets</em>

Step-by-step explanation:

If the whole stick of butter is cut into 6 pieces, and you can use one of those 6 pieces of butter per omelet, you can make 6 omelets with one stick of butter. Now, you have 12 sticks of butter, and you can make 6 omelets with each. 12 x 6= 72. I believe u can make 72 omelets in all.

Hope this helps dear!!

5 0
3 years ago
Answer to the question
Zepler [3.9K]

Answer:

x = 23

Step-by-step explanation:

AE = EC

so, 5x + 3 = 118

5x + 3 = 118

Bring +3 to the other side so -3

5x = 118 - 3

5x = 115

Bring 5 to the other side so:

x = 115 ÷ 5

x = 65

7 0
3 years ago
4-17 (-6)-3<br> Pls help <br> I know it equals -10 but I need a step by step answer
Elza [17]

Answer:

-10

Step-by-step explanation:

4-17-(-6)-3\\\\=4-17+6-3\\\\=(4+6)+(-17-3)\\\\=10+(-20)\\\\=10-20\\\\=-10

step two is the rule of signs for multiplication

6 0
3 years ago
Other questions:
  • WES collected 14,856 box tops. CES collected 26,982. How many more box tops did CES collect than WES?
    12·2 answers
  • 50 POINTS
    14·1 answer
  • What is one and a half times a right angle?
    14·1 answer
  • A box has a length of 15 in., a width of 7 in., and a height of 9 in. If Tara plans to cover the box with wrapping paper, how mu
    13·1 answer
  • (2-8i)^2 show work please
    14·1 answer
  • On a​ map, 1 inch equals 15 miles. Two cities are 3 inches apart on the map. What is the actual distance between the​ cities?
    9·1 answer
  • PLEASE HELP THIS IS MY FIRST QUESTION!! 100 POINTS
    15·2 answers
  • I am literally so sorry but I DON'T UNDERSTAND THIS IN MY MATH CLASS! PLEASE HELP
    5·2 answers
  • pls help immediately! this is due in 3 mins :/. (pls don’t give a link, i’ll give brainiest for the correct answer just pls help
    13·1 answer
  • Which of the following is an equivalent expression to the expression a1/3 / a1/4
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!