Probability Ch. 3.1

If you roll a pair of fair dice, what is the probability of getting a sum of 5?

{(1, 4, 2, 3)} = 4/36 = 0.1111111

If you roll a pair of fair dice, what is the probability of getting a sum of 12?

{(6)} = 1/36 = 0.0278

If you roll a pair of fair dice, what is the probability of getting a sum of 1?

0

In a multiple choice exam, there are 5 questions and 4 choices for each question (a, b, c, d). Nancy has not studied for the exam at all and decides to randomly guess the answers. What is the probability that: (c) she gets all of the questions right?

= (1/4)^5 = 0.0009765625

In a multiple choice exam, there are 5 questions and 4 choices (a, b, c, d) for each question. Nancy has not studied for the exam at all and decides to randomly guess all of the answers. What is the probability that: (b) she gets at least one question right?

= 1 - (3/4)^5 = 0.7626953125

In a multiple choice exam, there are 5 questions and 4 choices for each question (a, b, c, d). Nancy has not studied for the exam at all and decides to randomly guess the answers. What is the probability that: (a) the first question she gets right is the 5th question?

If the 5th is the first correct the answer pattern is wwwwc where w is "wrong" and c is "correct". P(wwwwc) = (3/4)^4*(1/4) = 81/1024 = 0.0791015625

An experienced teacher writes an exam so that, on average, about 5% of students will earn an A grade. If she has 50 students in her class and their performance is independent, what is the probability that at least one student gets an A?

It's 1 minus the probability that NO student gets an A. The probability that a student does not get an A is 100% - 5% = 95% = 0.95. The probability that 50 students do not get an A is 0.9550 = 0.0769449753. Therefore, the probability that at least one will get an A [P(at least one student will get an A)] is 1 - 0.0769449753 = 0.9230550247 or about 92.3% of the time.

If you flip a fair coin 10 times, what is the probability of getting all heads?

P (all heads in 10 flips) = (1/2)^10 = 0.00097656

If you flip a fair coin 10 times, what is the probability of getting all tails?

P (all tails in 10 flips) = (1/2)^10 = 0.00097656

If you flip a fair coin 10 times, what is the probability of getting at least one tails?

P (not getting all heads) = 1 - (1/2)^10 = 0.999023

Food allergies affect an estimated 7% of children under age 5 in the US. What is the probability that in a kindergarden class of 12 kids under age 5 at least one of them has food allergies? You may assume that the students in this class are a representative random sample from the population.

P(X >= 1) = 1- P(X = 0) = 1 - (1 - 0.07)^12 = 0.5814037025

Two guys walk into a bar; the third one ducks. If these three men acted independently, and the probability is 0.7 that a person who is about to walk into a bar instead ducks to avoid the bar, then what was the probability of observing the first two walking into the bar and the third ducking?

The product of the probabilities: 0.3 x 0.3 x 0.7 = 0.063