The situation has to be either A is true B is false, P_1=(0.75)×(0.2)=0.15 OrA is false and B is true P_2=(0.25)× (0.8) =0.2 Hence the required pr ...

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Standard XII

Mathematics

Axiomatic Approach

A speaks trut...

Question

$A$ speaks truth in $75$ % of the cases and $B$ in $80$ % cases. What is the probability that their statements about an incident do not match?

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Solution

The situation has to be either A is true B is false, $P_{1} = (0.75) \times (0.2) = 0.15$
Or
A is false and B is true
$P_{2} = (0.25) \times (0.8)$
$= 0.2$
Hence the required probability is $P_{1} + P_{2} = 0.2 + 0.15 = 0.35$

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A speaks truth in 75% of the cases and B in 80% cases. What is the probability that their statements about an incident do not match?

The situation has to be either A is true B is false, P1=(0.75)×(0.2)=0.15OrA is false and B is trueP2=(0.25)×(0.8)=0.2Hence the required probability is P1+P2=0.2+0.15=0.35

$A$ speaks truth in $75$ % of the cases and $B$ in $80$ % cases. What is the probability that their statements about an incident do not match?

The situation has to be either A is true B is false, $P_{1} = (0.75) \times (0.2) = 0.15$
Or
A is false and B is true
$P_{2} = (0.25) \times (0.8)$
$= 0.2$
Hence the required probability is $P_{1} + P_{2} = 0.2 + 0.15 = 0.35$