Foreign policy experts estimate that the probability is 0.65 that war will break

Question

Foreign policy experts estimate that the probability is 0.65 that war will break ous next year between two Middle East countries if either side significantly escalates its terrorist activities. Otherwise, the likelihood of war is estimated to be 0.05. Based on what has happened this year, the chance of terrorism reaching a critical level in the next 12 months are thought to be three in ten. What is the probability that the 2 countries will go to war? (the answer is 0.23,how can I get this answer?)

Explanation / Answer

This is a weighted probability problem. You must take eachpossible outcome and multiply it by the probability that theoutcome occurs. Then you simply add these weighted probabilitiestogether:

(.65)(.3) +(.05)(.7) = .195 + .035 = .23

Your weights will always add up to 1 (.3 + .7) = 1, but youroutcomes do not necessarily have to follow this rule.

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