13 The probability of an economic decline in the year 2008 i

13. The probability of an economic decline in the year 2008 is 0.23. There is a probability of 0.64 that we will elect a republican president in the year 2008. If we elect a republican president, there is a 0.35 probability of an economic decline. Let \'\'D\'\' represent the event of an economic decline, and \'\'R? represent the event of election of a Republican president. a. Are \'\'R\'\' and \'\'D\'\' independent events? b. What is the probability of a Republican president and economic decline in the year 2008? c. If we experience an economic decline in the year 2008, what is the probability that there will a Republican president? d. What is the probability of economic decline or a Republican president in the year 2008? Hint: You want to find P(D ?. R).

Solution

Answer :

1. D & R are not independent because P(D | R) = .35 which is not equal to P(D)
2. P(D n R) = P(D | R) P(R) = .35 x.64 = .224
3. P(R | D) = P(D n R) /P(D) = .224/.23 = .974
4. P(D u R) = P(D) + P(R) - P(D n R) = .23 + .64 - .224 = .646