Question

A man speaks truth 3 times out of 5. He says that in tossing 6 coins, two tails appear so what is the probability that this event is actually true ?

Solution

Let E represents the statement of a person , Now $$S_{1}$$ is the event of getting heads and $$S_{2}$$ is the event of not getting 2 heads on tossing 6 coins .$$\therefore P(S_{1}) = ^{6}C_{2} \left ( \dfrac{1}{2} \right )^{6-2} \left ( \dfrac{1}{2} \right )^{2}$$$$= ^{6}C_{2} \left ( \dfrac{1}{2} \right )^{6} = \dfrac{15}{64}$$$$P(S_{2}) = 1 - P(S_{1})$$$$= 1 - \dfrac{15}{64} = \dfrac{49}{64}$$$$= \dfrac{\frac{15}{64}\times \dfrac{3}{5}}{\frac{15}{64}\times\dfrac{3}{5} + \dfrac{49}{64}\times \dfrac{2}{5}} = \dfrac{45}{45 + 98} = \dfrac{45}{143}$$Maths

Suggest Corrections

0

Similar questions
View More

People also searched for
View More