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Addition rule for probability (basic)

One hundred students were surveyed about their preference between dogs and cats. The following two-way table displays data for the sample of students who responded to the survey.
PreferenceMaleFemaleTOTAL
Prefers dogs362056
Prefers cats102636
No preference268
TOTAL4852100
problem 1
Find the probability that a randomly selected student prefers dogs.
Enter your answer as a fraction or decimal.
P(prefers dogs)=
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi

Problem 2
In this sample, are the events "prefers dogs" and "prefers cats" mutually exclusive?
Choose 1 answer:

problem 3
Find the probability that a randomly selected student prefers dogs or prefers cats.
Enter your answer as a fraction or decimal.
P(prefers dogs or cats)=
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi

problem 4
In this sample, are the events "prefers dogs" and "female" mutually exclusive?
Choose 1 answer:

problem 5
Find the probability that a randomly selected student prefers dogs or is female.
Enter your answer as a fraction or decimal.
P(prefers dogs or is female)=
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi

Want to join the conversation?

  • blobby green style avatar for user elve5895
    I am eternally confused by wording (perhaps being ESL?). In the question: In this sample, are the events "prefers dogs" and "prefers cats" mutually exclusive? If someone likes both cats and dog equally, and for that reason chooses no preference, then doesn't the answer become no, not mutually exclusive? How do you know what they actually mean vs reading questions with the wrong assumptions about what they are even asking? Thanks!!
    (35 votes)
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  • starky sapling style avatar for user mario0104
    Why do I have to do homework if I can study at school? What is school for? Where is my freedom? I am willing to do my best at school but I also want to have time out of school.
    (0 votes)
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    • starky tree style avatar for user Drsusan.tutor
      Hi, Great job on working hard, good job on planning some fun, but be sure that you do not do more work than you need to in order to understand each class, score as well as you would like to and accomplish your goals. After college, I realized I worked myself much harder than I needed to and didn't enjoy my life as much as I wished. Work hard. Sleep hard. Enjoy the journey! Life is NOT in the "when I finish college," "when I get a job," "after I move," "after I get married," "after I retire," "when I get more time" etc. Life is in the journey. Enjoy every step of the way!
      (78 votes)
  • aqualine seed style avatar for user NatalieVigil22
    How do we tell when a question for probability is mutually exclusive?
    (5 votes)
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    • cacteye blue style avatar for user Jerry Nilsson
      If two events are mutually exclusive they can't both happen at the same time.

      If 𝐴 is the event that I drive a car,
      𝐵 is the event that I ride a bike,
      and 𝐶 is the event that I wear sunglasses,

      then 𝐴 and 𝐵 are mutually exclusive, but 𝐴 and 𝐶 are not mutually exclusive.
      (18 votes)
  • blobby green style avatar for user Kevin Zapata
    What exclusive means?
    (3 votes)
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  • blobby green style avatar for user cjohnson
    Are non-simplified answers acceptable or not?
    (3 votes)
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  • aqualine ultimate style avatar for user Natasha Lingam
    I am extremely confused with Mutually Exclusive and Not Mutually Exclusive. Is there an easier way to remember and differentiate between them?
    (5 votes)
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  • blobby green style avatar for user aryandesaiatl
    when do you need to subtract a and b
    (4 votes)
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    • piceratops seedling style avatar for user n. rock
      You need to subtract "a and b" when you are solving for a problem with overlap.
      For instance, in problem 5, a student could prefer dogs AND be female. When you calculate the probability that a student prefers dogs or is female, understand that each category (student that prefers dogs vs student that is female) contains members of the other category, as they are not mutually exclusive; some female students prefer dogs ('female students' includes some students who 'prefer dogs').
      Because of this overlap, you can't just add the two probabilities together-- that would over-represent the female students who like dogs. So you subtract that overlap ("a and b") once from your result.
      When A and B overlap: P(A or B) = P(A) + P(B) - P(A and B)
      (6 votes)
  • male robot johnny style avatar for user Mohamed Ibrahim
    There are 500 students in a high school senior class. Of these 500 students, 300 regularly wear a necklace to school, 200 regularly wear a ring, and 125 regularly wear a necklace and a ring. Using this information, answer each of the following questions.

    The probability of of a student wears a ring or a necklace was 3/4. Can someone explain this to me, how it's less than one while all students wear either ring or a necklace ?
    (2 votes)
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    • cacteye blue style avatar for user Jerry Nilsson
      125 of the students wear both a necklace and a ring.

      This means that 125 of the students who wear a necklace are also included in the group of students who wear a ring.

      So, when saying that the number of students who wear a necklace or a ring is 200 + 300 = 500, we actually count those 125 students twice!

      In order to make up for this mistake we must now subtract 125,
      and so the correct number of students who wear a necklace or a ring is
      500 − 125 = 375

      Thus, the proportion of students who wear a necklace or a ring is
      375∕500 = 3∕4

      – – –

      Also, by using the given information, we can construct the following two-way table:
      Ring No Ring TOTAL
      Necklace 125 175 300
      No Necklace 75 125 200
      TOTAL 200 300 500

      The number of students who wear...
      ...a necklace and a ring = 125
      ...a necklace and no ring = 175
      ...a ring and no necklace = 75

      Thereby, the number of students who wear a necklace or a ring =
      = 125 + 175 + 75 = 375
      (9 votes)
  • blobby green style avatar for user osbornconnor
    i do school at home because of the corona virus, and i don't care if i spell things wrong
    (5 votes)
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  • leafers ultimate style avatar for user Owen
    How do you solve the last question I don't understand it
    (3 votes)
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