Posted by sand on Sunday, January 22, 2012 at 4:45am.
Consider a collection of biased coins, each showing Heads with probability and Tails with probability , independently of the others. The coins are tossed and all coins showing Heads are collected together and tossed again. Write down an expression for the probability mass function of the random variable representing the number of Heads that turn up in the second round of tosses. Hint: Condition on the results of the first round of tosses using the “total probability" formula.

MathProbability  sand, Sunday, January 22, 2012 at 4:53am
Consider a collection of n biased coins, each showing Heads with probability p and Tails with probability 1p , independently of the others. The coins are tossed and all coins showing Heads are collected together and tossed again. Write down an expression for the probability mass function of the random variable representing the number of Heads that turn up in the second round of tosses. Hint: Condition on the results of the first round of tosses using the “total probability" formula.
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