# Probability-Bayes' Theorem and Applications (ISS Statistics Paper I (New 2016 MCQ Pattern)): Questions 4 - 5 of 5

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## Question number: 4

» Probability » Bayes' Theorem and Applications

### Question

Suppose a certain drug test is 99 % sensitive and 99 % specific, that is, the test will correctly identify a drug user as testing positive 99 % of the time, and will correctly identify a non-user as testing negative 99 % of the time. Let’s assume a corporation decides to test its employees for drug use, and that only 0.5 % of the employees actually use the drug. The probability that, given a positive drug test, an employee is actually a drug user is conducted using Bayes’ theorem. Can we say Bayes’ theorem gives correct result?

### Choices

Choice (4) | Response | |
---|---|---|

a. | Information insufficient | |

b. | Yes always | |

c. | Not always | |

d. | Can’t make any claim |

## Question number: 5

» Probability » Bayes' Theorem and Applications

### Question

Suppose there is a school with 40 % boys and 60 % girls as its students. The female students wear trousers or skirts in equal numbers; the boys all wear trousers. An observer sees a (random) student from a distance, and what the observer can see is that this student is wearing trousers. What is the probability this student is a girl?

### Choices

Choice (4) | Response | |
---|---|---|

a. | 0.552 | |

b. | 0.250 | |

c. | 0.428 | |

d. | Question does not provide sufficient data or is vague |