A fair coin is tossed 100 times. The event that the number of heads obtained is less than 35 is denoted by A.

By using a suitable approximation to the binomial distribution, calculate the probability of A.

The event that A occurs more than 3 times when 2000 such coins are each tossed 100 times is denoted by B.

By using another suitable approximation, calculate probability of B.

Also calculate the probability that B occurs exactly 3 times when 2000 such coins are each tossed 100 times on everyday of a given week.

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