# Probability

$P = \dfrac{\text{number of favorable ways}}{\text{total number of ways}}$

## Find the probability that somebody is healthy given that they have positive test result?

**Problem**

A disease is known to affect 1 in 10,000 people. A screening test for the disease shows a positive result for 99% of the people with the disease. The test also shows positive for 2% of people who do not have the disease. Find the probability that somebody is healthy given that they have positive test result?

A. 99.51% | C. 46.32% |

B. 12.32% | D. 78.36% |

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## What is the probability that 4 depth charges will sink the submarine?

**Problem**

Assume that a single depth charge has a probability of 1/2 of sinking a submarine, 1/4 of damage and 1/4 of missing. Assume also that two damaging explosions sink the sub. What is the probability that 4 depth charges will sink the sub?

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**Problem**

A coin is so unbalanced that you are likely to get two heads in two successive throws as you are to get tails in one. What is the probability of getting heads in a single throw?

A. 0.168 | C. 0.681 |

B. 0.618 | D. 0.816 |

**Problem**

The local weather forecaster says “no rain” and his record is 2/3 accuracy of prediction. But the Federal Meteorological Service predicts rain and their record is 3/4. With no other data available, what is the chance of rain?

A. 3/5 | C. 1/6 |

B. 1/4 | D. 5/12 |

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## Survival Probability Of The 6th Fly that Attempt To Pass A Spider

**Problem**

A spider eats three flies a day. Until he fills his quota, he has an even chance of catching any fly that attempts to pass. A fly is about to make the attempt. What are the chances of survival, given that five flies have already made the attempt today?

A. 1/2 | C. 3/4 |

B. 1/4 | D. 2/3 |

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## Probability That 1, 2, 3, 4 of the Recruits Will Receive the Correct Size of Boots

**Situation**

Four army recruits went to the supply room to get their military boots. Their shoe sizes were 7, 8, 9 & 10. The supply officer, after being informed of their sizes, prepared the four pairs of boots they need. If the boots are handed to each of the four recruits at random, what is the probability that...

- exactly 3 of them will receive the correct shoe size?
A. 1/16 C. 1/12 B. 1/24 D. 0 - all of them will receive the correct shoe size?
A. 1/16 C. 1/12 B. 1/24 D. 0 - none of them will receive the correct shoe size
A. 3/8 C. 1/16 B. 23/24 D. 5/12

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**Problem**

A box contains 5 defective and 195 non-defective cell phones. A quality control engineer selects 2 cell phones at random without replacement. What is the probability that exactly 1 is defective?

A. 0.0190 | C. 0.0390 |

B. 0.0490 | D. 0.0290 |

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**Problem**

An engineering company prepares an estimate for a job. The cost of preparing the estimate is Php10,000. The amount of profit over and above the Php10,000 is Php25,000 if their estimate is accepted. The probability that their estimate will be accepted 0.7 and the probability that their estimate will not be accepted is 0.3. What is the expected profit?

A. Php12,500 | C. Php14,500 |

B. Php13,500 | D. Php10,500 |

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**Problem**

Smith and Jones, both 50% marksmen, decide to fight a duel in which they exchange alternate shots until one is hit. What are the odds in favor of the man who shoots first?

A. 1/3 | C. 2/3 |

B. 1/2 | D. 1/4 |

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**Situation**

If a chord is selected at random on a fixed circle what is the probability that its length exceeds the radius of the circle?

- Assume that the distance of the chord from the center of the circle is uniformly distributed.
A. 0.5 C. 0.866 B. 0.667 D. 0.75 - Assume that the midpoint of the chord is evenly distributed over the circle.
A. 0.5 C. 0.866 B. 0.667 D. 0.75 - Assume that the end points of the chord are uniformly distributed over the circumference of the circle.
A. 0.5 C. 0.866 B. 0.667 D. 0.75

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