Probability

Problem 1

Two fair 4-sided dice are rolled and the values added together.  Find the probability mass function for the sum, the probability that the sum is at least 5, and the probability that the sum is at least 3.

Problem 2

You are taking a 5 question multiple choice test and have a 90% chance of getting each question right, what is the probability you will get 4 or more correct?

Problem 3

You are flipping a fair coin 8 times.  Given that you got at least 6 heads, what is the probability you got 7 or more?

Problem 4

Find the value of c which makes f(x)=({{{, ({{(1/3), x=1}, {(1/2), x=2}, {c, x=3}})}})  a valid probability mass function.  For this value of c find the mean and standard deviation.

Problem 5

A lightbulb has a mean lifetime of 5 years.  Find the probability it will last between 4 and 6 years.

Problem 6

Given that a point (x,y) lies in the square [0,2]×[0,2], what is the probability that x≥4-2y?

Problem 7

Check that the function f(x)=({{{, ({{(3/2)(x^2)-(3/4)(x^3), 0≤x≤2}, {0, otherwise}})}})  is a valid probability density function.  Use it to determine P(0≤x≤1) and P(1≤x≤2).

Problem 8

For the probability density function given by the graph below, find P(x≤3), P(2≤x≤4), and P(x>6 | x>4).

Plot[Evaluate[PDF[ TriangularDistribution[ {1,7},3],x]], {x,0,8}, Ticks-> {Range[8], Range[ 0, 1/3, 1/12]}, Filling-> Axis]

Problem 9

On a 100 question multiple choice test you have an 80% chance of getting any given question correct.  Estimate the probability your score would be between a 72 and 84.