A coin is tossed n times. a) What is the probability that exactly k heads occur? b) What is the probability that at most two heads occur? Type in your answers below in terms of k and n. As a student of computer science, your typeset answer should be an accurate use of the characters (parentheses, slash, exponent symbol, etc).

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A coin is tossed n times.  a) What is the probability that exactly k heads occur?  b) What is the probability that at most two heads occur?  Type in your answers below in terms of k and n. As a student of computer science, your typeset answer should be an accurate use of the characters (parentheses, slash, exponent symbol, etc).

escumantsu · Accepted Answer

Step 1  Given Data : A coin is tossed n times.  To Find: a) Probability that exactly k heads occur  b) Probability that at most two heads occur  On tossing a coin, either heads comes or tails  So, total number of possible Outcomes (one head + one tail)=2  Probability of getting head =Number of headTotal number of outcomes  Probability of getting head: P(H)=12  Similarly:  Probability of getting tail =Number of TailTotal number of outcomes  Probability of getting tail: P(T)=12  Step 2 if the coin is toss n times, then apply the Binomial Probability  Binomial Probability: It refers to the probability of exactly x successes on n repeated trials in an experiment which has two possible outcomes.  Probability =nCx⋅px⋅(1−p)n−x  In the given data :  p is the probability of getting head : p=12  for getting for k heads, i.e. x=k  Substitute the value :  Probability of getting  for k heads: P(k heads) =nCk⋅pk⋅(1−p)n−k  P(k heads) =nCk⋅pk⋅(1−p)n−k  P(k heads) =nCk(12)k(1−12)n−k  P(k heads) =nCk(12)k(12)n−k  Step 3  Probability for at-most two heads occur: x≤2  Probability for at-most two heads occur = probability for 0 head + probability for 1 head + probability of 2 head  Probability for atmost two head =nC0⋅p0⋅(1−p)n−0+nC1⋅p1⋅(1−p)n−1  Probability for atmost two head =nC0⋅1⋅(12)n+nC1⋅(12)⋅(12)n−1+nC2⋅(12)2⋅(12)n−2  Probability for atmost two head =nC0⋅(12)n+nC1⋅(12)n+nC2⋅(12)n  Probability for atmost two head

A coin is tossed n times. a) What is the probability that exactly k heads oc

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