The probability of an economic decline in the year 2020 is 0.23. There is a prob

Question

The probability of an economic decline in the year 2020 is 0.23. There is a probability of 0.64 that we will elect a republican president in the year 2020. 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. Use this information to answer the following four questions:

1 Are R and D independent events?

2 What is the probability of electing a Republican president and an economic decline in 2020?

3 If we experience an economic decline in 2016, what is the probability that a Republican president will have been elected in 2020?

4 What is the probability of economic decline or a Republican president elected in 2020 or both?

Explanation / Answer

Ans: Economic decline=D

Election of Republican president=R

P(D)=0.23

P(R)=0.64

P(D/R)=0.35

1)For two events to be independent:

P(D and R)=P(D)*P(R)

P(D)*P(R)=0.23*0.64=0.1472

P(D/R)=P(D and R)/P(R)

0.35=P(D and R)/0.64

P(D and R)=0.35*0.64=0.224

P(D and R) is not equal to P(D)*P(R),hence not independent.

2)As we know

P(D/R)=P(D and R)/P(R)

0.35=P(D and R)/0.64

P(D and R)=0.35*0.64=0.224

3)P(R/D)=[P(D/R)*P(R)]/P(D)=P(D and R)/P(D)

=(0.35*0.64)/0.23

=0.9739

4)P(D or R)=P(D)+P(R)-P(D and R)

=0.23+0.64-0.224

=0.646

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