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You are going to have a quiz with 5 true/false questions next Friday. You
want to find the probability of passing the quiz, if you guess on each
question.
Create a simulation that would represent this situation and complete 10
trials. Show all of your work for full credit.

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If you have 10 choices. You have about a 50 50 of passing or failing. Your chances would be 5/10 Wich would simplify to 1/2
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Based on the binomial probability principle, the probability of passing the quiz if all answers are guessed [tex] P(x = k) = 10Ck \times 0.50^{k} \times 0.50^{10-k} [/tex]

Let :

  • Number of questions passed = k
  • Number of trials, n = 10
  • Probability of success, p = 1/2 = 0.50
  • q = 1 - p = 1 - 0.50 = 0.50

Using the binomial probability relation :

  • [tex] P(x = x) = nCx \times p^{x} \times q^{n-x} [/tex]

  • x = k

Substituting the values into the relation :

[tex] P(x = k) = 10Ck \times 0.50^{k} \times 0.50^{10-k} [/tex]

Hence, the required probability expression is [tex] P(x = k) = 10Ck \times 0.50^{k} \times 0.50^{10-k} [/tex]

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