Question

Example:5

Following table shows a random sample of 100 hikers and the areas of hiking they prefer.

Sex       The Coastline      Near Lakes and Streams      On Mountain Peaks        Total

Female   18                                    16                                           11                                45

Male       16                                    25                                           14                                55

Total       34                                    41                                           25                               100

a. Are the events "being female" and "preferring the coastline" independent events?

Let F = being female and let C = preferring the coastline.

1. Find P(F ∩ C) =………………..

2. Find P(F)P(C)=……………………

Are these two numbers the same? If they are, then F and C are independent. If they are not, then F and C are not independent.

b. Find the probability that a person is male given that the person prefers hiking near lakes and streams. Let M =being male, and let L = prefers hiking near lakes and streams.

1. What word tells you this is a conditional?

      2. Fill in the blanks and calculate the probability: P(___ | ___) = ___.

      3. Is the sample space for this problem all 100 hikers? If not, what is it?

c. Find the probability that a person is female or prefers hiking on mountain peaks. Let F = being female, and let P = prefers mountain peaks.

      1. Find P(F)=……………..

      2. Find P(P)=……………..

      3. Find P(F ∩ P) =.…………...

      4. Find P(F ∪ P) =……………..

Answer 1