Math Problem Statement

Harry walks to the parking lot after class and notices the make of each car and calculates the following probabilities. The probability of seeing a Ford is 0.24, Honda is 0.23, Toyota is 0.25, Chevy is 0.13, and Kia is 0.15. Calculate the probability of the following: a) A Ford or Toyota. b) Any make other than a Honda

Solution

To calculate these probabilities, we use basic probability rules.

a) Probability of seeing a Ford or Toyota

The events "seeing a Ford" and "seeing a Toyota" are mutually exclusive (i.e., a car cannot be both a Ford and a Toyota). Therefore, the probability of seeing a Ford or a Toyota is the sum of the individual probabilities:

P(Ford or Toyota)=P(Ford)+P(Toyota)P(\text{Ford or Toyota}) = P(\text{Ford}) + P(\text{Toyota})

Given:

  • P(Ford)=0.24P(\text{Ford}) = 0.24
  • P(Toyota)=0.25P(\text{Toyota}) = 0.25

P(Ford or Toyota)=0.24+0.25=0.49P(\text{Ford or Toyota}) = 0.24 + 0.25 = 0.49

So, the probability of seeing a Ford or Toyota is 0.49.


b) Probability of seeing any make other than a Honda

This is the complement of the event "seeing a Honda." The complement rule states that the probability of an event not occurring is 1P(Honda)1 - P(\text{Honda}).

Given:

  • P(Honda)=0.23P(\text{Honda}) = 0.23

P(Not Honda)=10.23=0.77P(\text{Not Honda}) = 1 - 0.23 = 0.77

So, the probability of seeing any make other than a Honda is 0.77.


Let me know if you need further explanation on any of these concepts.


Here are some related questions you might consider:

  1. What is the probability of seeing a Kia or Chevy?
  2. What is the probability of seeing any car other than a Ford?
  3. What is the probability of seeing a Toyota and not a Honda?
  4. What is the probability of seeing a Ford, Honda, or Kia?
  5. What is the probability of seeing a Chevy or any make other than a Toyota?

Tip: The complement rule P(not A)=1P(A)P(\text{not A}) = 1 - P(A) is a handy tool for quickly calculating probabilities of events not occurring.

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Math Problem Analysis

Mathematical Concepts

Probability
Complementary Events
Mutually Exclusive Events

Formulas

P(A or B) = P(A) + P(B) for mutually exclusive events
P(Not A) = 1 - P(A)

Theorems

Complement Rule
Addition Rule for Mutually Exclusive Events

Suitable Grade Level

Grades 9-10