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The probability that A speaks truth is 4/5, while this probability for B is 3/4. The probability that they contradict each other when asked to speak on a fact is

  • Option 1)

    7/20

  • Option 2)

    1/5

  • Option 3)

    3/20

  • Option 4)

    4/5

 

Answers (1)

As we learnt in 

Probability of occurrence of an event -

Let S be the sample space then the probability of occurrence of an event E is denoted by P(E) and it is defined as 

P\left ( E \right )=\frac{n\left ( E \right )}{n\left ( S \right )}

P\left ( E \right )\leq 1

P(E)=\lim_{n\rightarrow\infty}\left(\frac{r}{n} \right )

 

 

- wherein

Where n repeated experiment and E occurs r times.

 

Probability of A speakig truth , P(AT) =  \frac{4}{5}

Probability of F speakig false  P (AF) =  \frac{1}{5}

Probability of B speakig truth P (BT) = \frac{3}{4}

Probability of B speakig truth false P (BF) = \frac{1}{4}

Elements where they contradict = \left ( AT, BF \right ), \left ( AF, BT \right )

Probability = \frac{4}{5}\times \frac{1}{4}+\frac{1}{5}\times \frac{3}{4}

= \frac{1}{5}+\frac{3}{20}

= \frac{7}{20}


Option 1)

7/20

Correct

Option 2)

1/5

Incorrect

Option 3)

3/20

Incorrect

Option 4)

4/5

Incorrect

Posted by

Sabhrant Ambastha

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