21 In Vancouver British Columbia the probability of rain dur

21. In Vancouver, British Columbia, the probability of rain during a winter day is 0.58, for a spring day is 0.38, for a summer day is 0.25, and for a fall day is 0.53. Each of these seasons lasts one quarter of the year.

a. What is the probability of rain on a randomly chosen day in Vancouver?

b. If you were told that on a particular day it was raining in Vancouver, what would be the probability that this day would be a winter day?

23. Imagine that a long stretch of a single-stranded DNA has 30% adenine, 25% thiamine, 15% cytosine, and 30% guanine. What is the probability of randomly drawing 10 adenines in a row in a sample of 10 randomly chose nucleotides?

Solution

a. Joint Probability : (0.58)*(0.38)*(0.25)*(0.53) =0.029203.

b. Conditional Probability : (0.029203)/0.58=0.0005035.

23. 0.03