Probability assignment help

Chapter 12 and 13: Probability Name:

1. Choose at random a person aged 15 to 44 years. Ask their age who they live with (alone, with spouse, with other persons). Here is the probability model for 12 possible answers:

15-19 20-24 25-34 35-44

Alone 0.001 0.011 0.031 0.030 With Spouse 0.001 0.023 0.155 0.216 With Others 0.169 0.132 0.142 0.089

(a) Why is this a legitimate probability model?

(b) What is the probability that the person chosen is a 15-19 year old who lives with others?

(c) What is the probability that the person is 15-19 years old?

(d) What is the probability that the person chosen lives with others?

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(e) List the outcomes that make up the event

A = {The person is either 15-19 years old or lives with others, or both}

(f) What is P(A)? Do you think P(A) is the sum of probabilities you found in parts (c) and (d)?

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2. Spell-checking software catches “non-word errors” that result in a string of letters that is not a word, as when “the” is typed as “teh.” When undergraduates are asked to type a 250-word essay (without spell-checking), the number X of nonword errors has the following distribution:

Value of X 0 1 2 3 4 Probability 0.1 0.2 0.3 0.3 0.1

(a) Is the probability space discrete or continuous?

(b) Write the event “at least one non-word error” in terms of X . What is the probability of this event?

(c) Describe the event “X ≤ 2” in words. What is its probability? What is the probability that X < 2?

3. Hacksaw’s Boats of St. Lucia takes tourists on a daily whale/dolphin watch cruise. Their brochure claims an 80% chance of siting a dolphin or a whale, and you can assume the sightings from day to day are independent.

(a) If you take the dolphin/whale watch cruise on two consecutive days, what is the probability you see a dolphin or a whale on both days?

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(b) If you take the dolphin/whale watch cruise on two consecutive days, what is the probability that you see a dolphin or a whale on at least one day? (HINT: First compute the probability that you don’t see a dolphin or whale on either day).

(c) If you want to have a 99% probability of seeing a dolphin or a whale at least once, what is the minimum number of days that you will need to take the cruise.

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4. You work at Rob’s pizza shop. You have the following information about the 7 pizza’s in the oven: 3 of the 7 have thick crust, and of these 1 has only sausage and 2 have only mushrooms; the remaining 4 pizzas have regular crust, and of these 2 have only sausage and 2 have only mushrooms. Choose a pizza at random from the oven.

(a) Are the events{getting a thick crust pizza}and{getting a pizza with mushrooms} independent? Justify your answer with a computation.

(b) You add an eighth pizza to the oven. This pizza has thick crust with only cheese. Now are the events{getting a thick crust pizza} and{getting a pizza with mushrooms} independent? Justify your answer with a computation.

(c) What is the probability of getting a thick crust pizza, given that it has sausage?