Math Problem Statement

Calculate P(car, bus, or bicycle). Give your answer as a decimal.

Solution

To solve this question, we need to calculate P(car, bus, or bicycle)P(\text{car, bus, or bicycle}), which involves summing up the probabilities of each mode of transport:

Given:

  • P(car)=47%=0.47P(\text{car}) = 47\% = 0.47 (convert percentage to decimal)
  • P(bus)=0.13P(\text{bus}) = 0.13
  • P(bicycle)=310=0.3P(\text{bicycle}) = \frac{3}{10} = 0.3

Calculation:

The probability of traveling by car, bus, or bicycle is:

P(car, bus, or bicycle)=P(car)+P(bus)+P(bicycle)P(\text{car, bus, or bicycle}) = P(\text{car}) + P(\text{bus}) + P(\text{bicycle})

P(car, bus, or bicycle)=0.47+0.13+0.3P(\text{car, bus, or bicycle}) = 0.47 + 0.13 + 0.3

P(car, bus, or bicycle)=0.90P(\text{car, bus, or bicycle}) = 0.90

Final Answer:

P(car, bus, or bicycle)=0.9P(\text{car, bus, or bicycle}) = 0.9


Would you like a further breakdown or have any related questions?


Related Questions:

  1. What is the probability of not traveling by car, bus, or bicycle?
  2. How would the answer change if an additional mode of transport with P(walk)=0.1P(\text{walk}) = 0.1 was included?
  3. What percentage of people traveled by car or bus only?
  4. If there were 1000 people surveyed, how many traveled by bicycle?
  5. Can probabilities ever exceed 1? Why or why not?

Tip:

When working with probabilities, always ensure that the sum of all outcomes equals 1 to verify your calculations!

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Math Problem Analysis

Mathematical Concepts

Probability
Addition Rule of Probabilities
Conversion of Percentages to Decimals

Formulas

P(A or B or C) = P(A) + P(B) + P(C)

Theorems

Addition Rule for Mutually Exclusive Events

Suitable Grade Level

Grades 7-9