Question

A student has just been given a 10-question multiple-choice quiz. Each question has five answers, of which only one is correct. The student has not attended class recently, and doesn't know any of the answers. Assume that guesses are made on all ten questions, find the indicated probability. (Round your answer to three decimal places.) What is the probability that the student will answer all questions incorrectly?

Answer #1

This question pertains to the binomial distribution.

Let X be the number of correct answers out of a possible 10 questions.

Then

**with**

We need to find P(X=0)

**Calculations**

X |
P(X=x) |

0 | 0.1073742 |

1 | 0.2684355 |

2 | 0.3019899 |

3 | 0.2013266 |

4 | 0.0880804 |

5 | 0.0264241 |

6 | 0.0055050 |

7 | 0.0007864 |

8 | 0.0000737 |

9 | 0.0000041 |

10 | 0.0000001 |

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