Math Problem Statement

Voting for a city proposition Favor Oppose Subtotal Likely to vote 350 275 625 Unlikely to vote 150 105 255 Subtotal 500 380 880 Find P( Oppose AND Likely )

Examples: For single event or conditional probabilities, enter answer as one unreduced fraction, using / for division using no spaces between it and the numbers. For example, 3 divided by 4 would be entered 3/4.

For the multiplication rule P(A and B)=P(A)P(B|A), enter answer as a product of two unreduced fractions, using / for division and * for multiplication, using no spaces between the operations and the numbers . For example, three fourths multiplied by five thirds would be entered 3/45/3.

For the addition rule P(A or B)=P(A)+P(B)-P(A and B), enter answer as a string of 3 fractions, using / for division and + for addition and - for subtraction, using no spaces between the operations and the numbers . For example, three eighths plus four eighths minus two eighths would be entered 3/8+4/8-2/8.

Solution

To find P(Oppose AND Likely)P(\text{Oppose AND Likely}), we need to look at the probability that a voter both opposes the proposition and is likely to vote.

From the table:

  • The number of people who are both likely to vote and oppose the proposition is 275.
  • The total number of people surveyed is 880.

Thus, P(Oppose AND Likely)=275880P(\text{Oppose AND Likely}) = \frac{275}{880}.

The answer in the required format is:

275880\frac{275}{880}

Let me know if you'd like more details or have questions!


  1. What is P(Oppose)P(\text{Oppose}) for the entire group?
  2. How do you find P(Likely to Vote)P(\text{Likely to Vote})?
  3. What is P(Favor AND Unlikely to Vote)P(\text{Favor AND Unlikely to Vote})?
  4. How would you calculate P(Oppose OR Likely)P(\text{Oppose OR Likely})?
  5. Can we find the probability that someone favors the proposition given they are likely to vote?

Tip: When dealing with "AND" probabilities, focus on the overlapping data for both events and divide by the total in the dataset.

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Math Problem Analysis

Mathematical Concepts

Probability
Joint Probability

Formulas

P(A AND B) = (Number of favorable outcomes for A and B) / (Total number of outcomes)

Theorems

Multiplication Rule of Probability

Suitable Grade Level

Grades 9-12