SOLUTION: The ODDS against a certain event happening tomorrow are 7 to 3, and the odds in favor of another event, independent of the former, happening tomorrow are 8 to 5. Find the probabili

Algebra ->  Probability-and-statistics -> SOLUTION: The ODDS against a certain event happening tomorrow are 7 to 3, and the odds in favor of another event, independent of the former, happening tomorrow are 8 to 5. Find the probabili      Log On


   

Question 1028531: The ODDS against a certain event happening tomorrow are 7 to 3, and the odds in favor of another event, independent of the former, happening tomorrow are 8 to 5. Find the probability that at least one of these two events will happen tomorrow. Express your answer as a common fraction reduced to lowest terms.
Answer: 19/26

Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
P(Event 1) = 3%2F%287%2B3%29+=+3%2F10+
P(Event 2) = 8%2F%285%2B8%29+=+8%2F13
==> P(Event 1 ∪ Event 2) = P(Event 1) + P(Event 2) - P(Event 1 ∩ Event 2)
<==>P(Event 1 ∪ Event 2) = P(Event 1) + P(Event 2) - P(Event 1)*P(Event 2)
= 3%2F10+%2B+8%2F13+-+%283%2F10%29%288%2F13%29+=+19%2F26