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Precalculus

Course: Precalculus > Unit 8

Lesson 1: Venn diagrams and the addition rule
Math
Precalculus
Probability and combinatorics
Venn diagrams and the addition rule
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Addition rule for probability (basic)

AP.STATS:
VAR‑4 (EU)
,
VAR‑4.C (LO)
,
VAR‑4.C.2 (EK)
,
VAR‑4.E (LO)
,
VAR‑4.E.4 (EK)
 CCSS.Math:
HSS.CP.B.7
Google Classroom
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, left parenthesis, start text, p, r, e, f, e, r, s, space, d, o, g, s, end text, right parenthesis, equals
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

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, left parenthesis, start text, p, r, e, f, e, r, s, space, d, o, g, s, space, o, r, space, c, a, t, s, end text, right parenthesis, equals
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

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, left parenthesis, start text, p, r, e, f, e, r, s, space, d, o, g, s, space, o, r, space, i, s, space, f, e, m, a, l, e, end text, right parenthesis, equals
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

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  • blobby green style avatar for user elve5895
    Posted 5 years ago. Direct link to elve5895's post “I am eternally confused b...”
    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!!
    (25 votes)
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  • starky sapling style avatar for user mario0104
    Posted 6 years ago. Direct link to mario0104's post “Why do I have to do homew...”
    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
      Posted 5 years ago. Direct link to Drsusan.tutor's post “Hi, Great job on working ...”
      Incredible Answer
      Great Answer
      Good Answer
      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!
      (58 votes)
  • blobby green style avatar for user cjohnson
    Posted 6 years ago. Direct link to cjohnson's post “Are non-simplified answer...”
    Are non-simplified answers acceptable or not?
    (3 votes)
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  • aqualine seed style avatar for user NatalieVigil22
    Posted 3 years ago. Direct link to NatalieVigil22's post “How do we tell when a que...”
    How do we tell when a question for probability is mutually exclusive?
    (3 votes)
    Default Khan Academy avatar avatar for user
  • aqualine ultimate style avatar for user Natasha Lingam
    Posted 4 years ago. Direct link to Natasha Lingam's post “I am extremely confused w...”
    I am extremely confused with Mutually Exclusive and Not Mutually Exclusive. Is there an easier way to remember and differentiate between them?
    (4 votes)
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  • blobby green style avatar for user osbornconnor
    Posted 3 years ago. Direct link to osbornconnor's post “i do school at home becau...”
    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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  • blobby green style avatar for user Kevin Zapata
    Posted 8 months ago. Direct link to Kevin Zapata's post “What exclusive means?”
    What exclusive means?
    (2 votes)
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  • male robot johnny style avatar for user Mohamed Ibrahim
    Posted 3 years ago. Direct link to Mohamed Ibrahim's post “There are 500 students in...”
    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 ?
    (1 vote)
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    • cacteye blue style avatar for user Jerry Nilsson
      Posted 3 years ago. Direct link to Jerry Nilsson's post “125 of the students wear ...”
      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
      (6 votes)
  • leafers ultimate style avatar for user Owen
    Posted 24 days ago. Direct link to Owen's post “How do you solve the last...”
    How do you solve the last question I don't understand it
    (2 votes)
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  • blobby green style avatar for user Sowmya Sangeetham
    Posted 3 years ago. Direct link to Sowmya Sangeetham's post “For the question : "Find ...”
    For the question : "Find the probability that a randomly selected student prefers dogs or is female."
    Why they took the ones with "No Preference". It should be 56/100 + 46/100 - 20/100 right?
    (1 vote)
    Default Khan Academy avatar avatar for user