There are 3 questions Please provide detailed answers 3 One

There are 3 questions. Please provide detailed answers

3. One of a die and a coin (sides 0 and 1) is selected at random and tossed. (a) If the outcome is 0, what is the probability the coin was chosen? (b) If the outcome is 1, what is the probability the coin was chosen? 4. An HIV test is known to be 98% accurate (i.e. the probability of a correct diagnosis is 0.98) and 0.5% of the population is known to be HIV positive. (a) What is the probability that a random person will test positive? (b) If a person selected at random does test positive, what is the probability that he is infected? Bonus. A gambler has three coins in his pocket, one is normal, one is head-head and the third is tail-tail. He picks one at random and tosses it and it shows heads. The gambler says that since you now know the coin is either head-head or head-tail the odds that the other side is tails is 1/2. Is this true?

Solution

3) a) 1

b) 0.5

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4) a)0.98(0.05) = 0.049

b)0.98\\

Bonus: True