Question

A is known to speak truth \[5\] out of \[7\] times. What is the probability that \[A\] reports that it is a \[7\] when a die is thrown?

Answer 1

Hint: Here it is given that A speaks truth 5 out of 7 times. Here we should find the probability that A speaks lie since 7 cannot be thrown in a die. To find the probability of lying we subtract the probability of truth from the total probability.

Formula used: Let us consider, total outcomes of an event is \[n\] and outcome of a particular event is \[m\]. So, the probability is \[\dfrac{m}{n}.\]

Complete step-by-step answer:
It is given that A is known to speak truth \[5\] out of \[7\] times. We have to find the probability that \[A\] reports that it is a \[7\] when a die is thrown.
Since 7 cannot be thrown in a die we should find the probability of A speaking lie.
We know that the total probability of an event is \[1\].
If the total outcome of an event is \[n\] and outcome of a particular event is \[m\]. The probability of getting the particular event is \[\dfrac{m}{n}.\]
Here we have $(m=5)$ & $(n=7)$
Therefore the probability of speaking the truth is \[\dfrac{5}{7}\].
We can find the probability of lie by subtracting the probability of truth from the total probability,
Hence, the probability of lie \[1 - \dfrac{5}{7} = \dfrac{2}{7}\]
Hence, the probability that \[A\] reports that it is a \[7\] when a die is thrown is \[\dfrac{2}{7}\] .

Additional information:
 Many events can't be predicted with total certainty. The best we can say is how likely they are to happen, using the idea of probability.
The probability of a certain event is \[1\].

Note: We should be careful that while finding the probability that \[A\] reports that it is a \[7\] when a die is thrown because it should be chosen as a lie. Since it is given the probability of truth
We can also use the fact that if A is speaking truth \[5\] out of \[7\] times then he speaks lie 2 out of 7 times, and thereby using this fact the probability of lie can be found.