Calculate exact and cumulative binomial probabilities for a biased coin.

Calculate exact and cumulative binomial probabilities for a biased coin.

5 marks
ProbabilityQuestionBank.pdf

The probability of obtaining heads on a biased coin is 0.18. The coin is tossed seven times.

  1. Find the probability of obtaining exactly two heads.[2]
  2. Find the probability of obtaining at least two heads.[3]

Solution:

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Answer:Let \(X\sim\operatorname{Bin}(7,0.18)\). Then \(P(X=2)=0.2523\) and \(P(X\ge2)=0.3677\).

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