(a) Suppose you have one fair coin, and one biased coin which lands Heads with probability...

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(a) Suppose you have one fair coin, and one biased coin which lands Heads with probability 4/5. You choose one of the coins at random and throw it three times independently. If it lands Heads all the three times, find the probability that the coin you picked is the fair one and comment. (b) Suppose coin R gives heads with probability & and coin B gives heads with probability .. They are tossed alternately and independently, starting off with the coin R. Find the probability that the first head is obtained on the coin R and comment. (c) A group of 80 boys and 80 girls is divided into two equal groups. Find the probability that each group will be equally divided into boys and girls. (d) Define Expectation of a random variable. Give an example of a random variable X for which 0 (a) Suppose you have one fair coin, and one biased coin which lands Heads with probability 4/5. You choose one of the coins at random and throw it three times independently. If it lands Heads all the three times, find the probability that the coin you picked is the fair one and comment. (b) Suppose coin R gives heads with probability & and coin B gives heads with probability .. They are tossed alternately and independently, starting off with the coin R. Find the probability that the first head is obtained on the coin R and comment. (c) A group of 80 boys and 80 girls is divided into two equal groups. Find the probability that each group will be equally divided into boys and girls. (d) Define Expectation of a random variable. Give an example of a random variable X for which 0