In: Statistics and Probability

1.)the chair of the board of directors says, "there is a 50% chance this company will earn a profit, a 30% chance it will lose money next quarter." a.) use an addition rule to find the probability the company will not lose money next quarter B.) use he complement rule to find the probability it will not lose money next quarter.

2.)suoose P(X_{1} )=.75 and
P(Y_{2}|X_{1})=.40. what is the joint probability
of X_{1} & Y_{2}

3.)An investor owns three common stocks. Each stock, independent of the others, has equally likely chances of (1) increasing in value. (2) decreasing in value, or (3) remaining same value. List the possible outcomes of this experiment. Estimate the probability at least two of the stocks increase in value.

1.)the chair of the board of directors says, "there is a 50% chance this company will earn a profit, a 30% chance it will lose money next quarter." a.) use an addition rule to find the probability the company will not lose money next quarter B.) use he complement rule to find the probability it will not lose money next quarter.

a)

Pr(neither lose nor profit) = 1 - 0.50 - 0.30 = 0.20

Using addition rule,

Pr(company will not lose money next quarter) = Pr(Profit) + Pr(neither lose nor profit)

Pr(company will not lose money next quarter) = 0.50 + 0.20 = 0.70

b)

Using the complement rule,

Pr(company will not lose money next quarter) = 1 - Pr(company will lose money next quarter)

Pr(company will not lose money next quarter) = 1 - 0.30 = 0.70

2)

Using the conditional probability law,

3)

For each stock, there are three possible outcomes, such that (1) increasing in value. (2) decreasing in value, or (3) remaining the same value

Hence total possible outcomes for three stocks = 3*3*3 = 27

Let A represents increasing in value, B represents decreasing in value, and C represents remaining the same value.

Outcome | Stock 1 | Stock 2 | Stock 3 |

1 | A | A | A |

2 | A | A | B |

3 | A | A | C |

4 | A | B | A |

5 | A | B | B |

6 | A | B | C |

7 | A | C | A |

8 | A | C | B |

9 | A | C | C |

10 | B | A | A |

11 | B | A | B |

12 | B | A | C |

13 | B | B | A |

14 | B | B | B |

15 | B | B | C |

16 | B | C | A |

17 | B | C | B |

18 | B | C | C |

19 | C | A | A |

20 | C | A | B |

21 | C | A | C |

22 | C | B | A |

23 | C | B | B |

24 | C | B | C |

25 | C | C | A |

26 | C | C | B |

27 | C | C | C |

(count the number of outcomes where 'A' appears 2 or 3 times then divide it by total number of outcomes = 27)

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