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February 21st, 2016, 12:27 PM   #1
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Discrete Probability Distributions

Can someone help me answer this? It's kind of lengthy but any help would be appreciated:

You have been assigned the duty of determining Air Force jet "readiness" to defend against a terrorist attack in the Washington DC area. There are 16 F-22a jet planes in the squadron that are to be scrambled in the event of a possible attack. "Readiness" is defined as "not less than 12 planes will launch on warning." Your aircraft mechanic staff have apprised you that, due to recent government cutbacks, there is a 30% chance that any given plane, among the 16, may not be flightworthy at a given instant because of maintenance.

Your task: determine the probability that your unit is "ready" to defend Washington DC from air attack. Ready is defined as 12 or more (which is also "not less than 12") can fly at any given instant. Note that you have the probability of a plane NOT flying at a given instant; consider what the probability is of a plane FLYING at a given instant, as you consider your task.

First hints: You need to determine the probability of readiness to answer this problem. You need to determine the probability of unreadiness. You need to think about compliments as well -- what is the compliment of readiness? What is the compliment of unreadiness? What does "12 or more" mean? What does "11 or less" mean in this problem?

a) Develop a complete discrete probability distribution for the 16 planes being ready to fly in this form

b) Develop a discrete cummulative probability distribution to answer the question of likelihood of 11 or less planes being ready to fly (
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February 21st, 2016, 01:45 PM   #2
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The description is extra wordy. The probability is given by a binomial distribution. The probability that exactly k will be ready is $\displaystyle P_k=\binom {16}{k}0.7^k*0.3^{16-k}$.

You want $\displaystyle \sum_{k=12}^{16}P_k$.
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February 21st, 2016, 03:23 PM   #3
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Thank you for the quick reply. It wants me to develop the distribution in this form:

X | P(x)

0 |

1 |

2 |

3 |

4 |

So how would I get started doing that?
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February 21st, 2016, 06:45 PM   #4
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Quote:
Originally Posted by Ore0Kidd View Post
Thank you for the quick reply. It wants me to develop the distribution in this form:

X | P(x)

0 |

1 |

2 |

3 |

4 |

So how would I get started doing that?
Plug in mathman's formula for each of these values...
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February 21st, 2016, 06:51 PM   #5
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Quote:
Originally Posted by 123qwerty View Post
Plug in mathman's formula for each of these values...
I'm not sure how to exactly plug them in. Could you show me one example to get me started? Thank you for your reply.

Sorry for my math stupidity, lol.
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February 21st, 2016, 10:50 PM   #6
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Originally Posted by Ore0Kidd View Post
I'm not sure how to exactly plug them in. Could you show me one example to get me started? Thank you for your reply.

Sorry for my math stupidity, lol.
For example, in the '0' column, plug in k = 0 into the first formula provided by mathman.
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