 Hi and welcome to the session. I am Shashi and I am going to help you with the following question. Question says, suppose that 5% of men and 0.25% of women have grey hair. A grey-haired person is selected at random. What is the probability of this person being male? Assume that there are equal number of males and females. Let us now start with the solution. First of all, let us define some events. Let event M represents that a male is chosen, event F represents that a female is chosen and event G represents that a grey-haired person is chosen. Now we are given in the question that assume that there are equal number of males and females. So probability that male is chosen is equal to 1 upon 2 and probability that female is chosen is also equal to 1 upon 2. We know selected person can be male or female. So total possible outcomes is equal to 2 and outcome favourable to selection of male is equal to 1. So probability of choosing a male is equal to 1 upon 2. Similarly probability that a female is chosen is also equal to 1 upon 2. Now we are also given that probability that a grey-haired person is chosen and it is known that a person is male is equal to 5% or we can say probability of event G when event M has already occurred is equal to 5 upon 100 which is further equal to 1 upon 20. We are also given probability that a grey-haired person is chosen when it is known that a person is female is equal to 0.25%. Or we can say probability of event G when event F has already occurred is equal to 0.25 upon 100. We know we can write 0.25% as 0.25 upon 100. Now this is further equal to 1 upon 400. Now we have to find the probability that the person is a male when it is known that the person chosen is grey-haired. Or we can say we have to find the probability of event M when event G has already occurred. Now according to Bayes' theorem probability of event M when G has already occurred is equal to probability of event M multiplied by probability of event G when event M has already occurred upon probability of event M multiplied by probability of event G when M has occurred plus probability of event F multiplied by probability of event G when F has already occurred. Now we know probability of event M is equal to 1 upon 2 probability of event F is equal to 1 upon 2 probability of event G when M has occurred is equal to 1 upon 20 and probability of event G when F has occurred is equal to 1 upon 400. Now substituting all these values in right hand side of this expression we get probability of event M when G has already occurred is equal to 1 upon 2 multiplied by 1 upon 20 upon 1 upon 2 multiplied by 1 upon 20 plus 1 upon 2 multiplied by 1 upon 400. Now this is further equal to 1 upon 40 upon 1 upon 40 plus 1 upon 800. Now adding these two terms in the denominator we get 21 upon 800 so we can write this expression is further equal to 1 upon 40 upon 21 upon 800. Now this is further equal to 1 upon 40 multiplied by 800 upon 21. Now we will cancel common factor 40 from numerator and denominator both and we get 20 upon 21 is equal to probability of event M when G has already occurred or we can say probability that the person is a male when it is known that the person chosen is a grey-haired person is equal to 20 upon 21. So this is our required answer. This completes the session. Hope you understood the solution. Take care and have a nice day.