An unbalanced coin weighted so that the probability of heads is . The coin is tossed ten times.
(a) What is the probability of getting exactly 6 heads?
(b) What is the probability of getting fewer than 3 heads?
The probability of getting exactly heads.
The probability of getting head in a biased coin is and the coin is tossed ten times.
The formula of probability of an event is given by,
Here, is the number of success required in number of trails, is the probability of success and is the probability of failure.
The formula for is given by,
The probability of getting head in a biased coin is so,
Sum of total probability is equal to so the probability of failure is,
Substitute for , for , for and for in above equation.
The probability of getting fewer than heads.
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