Answer
Verified
397.8k+ views
Hint:In this we apply the probability of happening an event and not happening of that particular event. So, the probability of A speaking truth is P (A) = $75\% $or \[\dfrac{3}{4}\]and not speaking truth or lie $P(\overline A )$ = $25\% $ or$\dfrac{1}{4}$. Similarly the probability of B speaking truth is P (B) = $80\% $ or $\dfrac{4}{5}$and not speaking truth is $P(\overline {B)} $= $20\% $ or$\dfrac{1}{5}$. In case of contradiction with each other is when A speaks truth and B speaks lie or A speaks lie and B speaks truth. For finding the probability we add both the situation and find the percentage.
Complete step-by-step answer:
Let A be Event that speaks the truth and B be Event that speaks the truth
So, the probability of A speaking truth P(A)= $75\% $
=$\dfrac{{75}}{{100}} = \dfrac{3}{4}$
The probability of B speaking truth P(B)= $80\% $
=$\dfrac{{80}}{{100}} = \dfrac{4}{5}$
We know $P(A)+P(\overline A )=1$ Hence,
Probability of A not speaking truth $P(\overline A )$= $1 - \dfrac{3}{4} = \dfrac{1}{4}$
Probability of B not speaking truth $P(\overline {B)} $ = $1 - \dfrac{4}{5}=\dfrac{1}{5}$
Now, A and B contradict each other=[A speaks truth and B speaks lie] or [A speaks lie and B speaks truth]
We will add both situation
= $P(A) \times P(\overline B ) + P(\overline A ) \times P(B)$
=\[(\dfrac{3}{4} \times \dfrac{1}{5}) + (\dfrac{1}{4} \times \dfrac{4}{5})\]
=$\dfrac{3}{{20}} + \dfrac{4}{{20}}$
=$\dfrac{7}{{20}}$
For percentage we multiply $\dfrac{7}{{20}}$ by $100\% $
=$(\dfrac{7}{{20}} \times 100)\% $
=$35\% $
So, the case when A and B contradicts is $35\% $.
The correct answer is C=$35\% $.
So, the correct answer is “Option C”.
Note:When there is a case of contradiction we must consider both the cases i.e. probability of happening of the event and probability not happening of the event. The probability of the event lies between 0 and 1, where 0 and 1 are included.
Complete step-by-step answer:
Let A be Event that speaks the truth and B be Event that speaks the truth
So, the probability of A speaking truth P(A)= $75\% $
=$\dfrac{{75}}{{100}} = \dfrac{3}{4}$
The probability of B speaking truth P(B)= $80\% $
=$\dfrac{{80}}{{100}} = \dfrac{4}{5}$
We know $P(A)+P(\overline A )=1$ Hence,
Probability of A not speaking truth $P(\overline A )$= $1 - \dfrac{3}{4} = \dfrac{1}{4}$
Probability of B not speaking truth $P(\overline {B)} $ = $1 - \dfrac{4}{5}=\dfrac{1}{5}$
Now, A and B contradict each other=[A speaks truth and B speaks lie] or [A speaks lie and B speaks truth]
We will add both situation
= $P(A) \times P(\overline B ) + P(\overline A ) \times P(B)$
=\[(\dfrac{3}{4} \times \dfrac{1}{5}) + (\dfrac{1}{4} \times \dfrac{4}{5})\]
=$\dfrac{3}{{20}} + \dfrac{4}{{20}}$
=$\dfrac{7}{{20}}$
For percentage we multiply $\dfrac{7}{{20}}$ by $100\% $
=$(\dfrac{7}{{20}} \times 100)\% $
=$35\% $
So, the case when A and B contradicts is $35\% $.
The correct answer is C=$35\% $.
So, the correct answer is “Option C”.
Note:When there is a case of contradiction we must consider both the cases i.e. probability of happening of the event and probability not happening of the event. The probability of the event lies between 0 and 1, where 0 and 1 are included.
Recently Updated Pages
Assertion The resistivity of a semiconductor increases class 13 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
How do you arrange NH4 + BF3 H2O C2H2 in increasing class 11 chemistry CBSE
Is H mCT and q mCT the same thing If so which is more class 11 chemistry CBSE
What are the possible quantum number for the last outermost class 11 chemistry CBSE
Is C2 paramagnetic or diamagnetic class 11 chemistry CBSE
Trending doubts
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Summary of the poem Where the Mind is Without Fear class 8 english CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
Write an application to the principal requesting five class 10 english CBSE
What organs are located on the left side of your body class 11 biology CBSE
What is the z value for a 90 95 and 99 percent confidence class 11 maths CBSE