GATE IT 2006 | Question: 1

Question

In a certain town, the probability that it will rain in the afternoon is known to be $0.6$. Moreover, meteorological data indicates that if the temperature at noon is less than or equal to $25°C$, the probability that it will rain in the afternoon is $0.4$. The temperature at noon is equally likely to be above $25°C$, or at/below $25°C$. What is the probability that it will rain in the afternoon on a day when the temperature at noon is above $25°C$?

• A. $0.4$
• B. $0.6$
• C. $0.8$
• D. $0.9$

Comments

Given,

P(A)=0.6

P(A')=0.4

P(A|<=25)=0.4

P(<=25)=0.5

P(>25)=0.5

P(A|>25)=?

P(A|>25)=P(A,>25)/P(>25)

P(A,>25)=?

 

P(A,<=25)=P(A|<=25)*P(<=25)

P(A,<=25)=0.4*0.5

P(A,<=25)=0.2

Law of total probability

P(A)=P(A,>25)+P(A,<=25)

0.6=P(A,>25)+0.2

P(A,>25)=0.4

P(A|>25)=P(A,>25)/P(>25)

P(A|>25)=0.4/0.5

P(A|>25)=0.8

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Ans

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In this Question I missed the Pr(rain) =0.6 which is given ..And I assume that how it is possible to solve this Question then I came across solution ..I got to know that I missed that part .

Answer 1

Answer: (C) 0.8