Question

Albertsons conducted a one-question customer survey of customers selected at random to evaluate satisfaction with length of time waiting to check out. The survey has six possible responses, and a customer choses exactly one response. The following table is the probability distribution based on the results of the survey.

Response |
Probability |

Very satisfied | 0.11 |

Somewhat satisfied | 0.36 |

Neither satisfied nor dissatisfied | 0.1 |

Somewhat dissatisfied | 0.05 |

Very dissatisfied | .05 |

Declined to respond |

Define the following events:

A = {customer is very satisfied}

B = {customer is somewhat satisfied}

C = {customer is neither satisfied nor dissatisfied}

What is the probability P(A or B or C)?

Express your answer in decimal form to 3 decimal places.

Answer #1

Given:

The probability distribution based on the results of the survey is

Response | Probability |

Very satisfied | 0.11 |

Somewhat satisfied | 0.36 |

Neither satisfied nor dissatisfied | 0.1 |

Somewhat dissatisfied | 0.05 |

Very dissatisfied | .05 |

Declined to respond |

Define the following events:

A = {customer is very satisfied}

B = {customer is somewhat satisfied}

C = {customer is neither satisfied nor dissatisfied}

P(A) = 0.11

P(B) = 0.36

P(C) = 0.10

The events A, B and C are independent events.

If A , B and C are independent events then

P(A or B or C) = P(A) + P(B) + P(c)

= 0.11 + 0.36 + 0.10

= 0.57

Therefore the probability P(A or B or C) is 0.570

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