Probability Equations Explained with Examples

According to the most recent national political poll, there is a 0.55 percent chance that a randomly chosen American is conservative, a 0.30 percent chance that they are liberal, and a 0.15 percent chance that they are middle-of-the-road. Assuming that these probabilities are accurate, answer the following questions pertaining to a randomly chosen group of 10 Americans. What is the probability that none are conservative?

Edmund Adams 2021-11-15

A batch of 500 containers for frozen orange juice contains 5 that are defective. Two are selected, at random, without replacement from the batch.
1) What is the probability that the second one selected is defective given that the first one was defective?
2) What is the probability that both are defective?
3) What is the probability that both are acceptable?

Maggenifh 2021-11-15

Calculate the following probabilities:
(a) The probability of taking 3 red balls from a bag containing 4 red balls, 5 blue balls, 6 green balls.
(b) The probability of tossing 5 coins and exactly getting 2 heads
(c) The probability of winning a game that requires you to throw exactly 2 one’s when throwing 5 dice

varaderiyw 2021-11-15

The probability of a player scoring a goal is 0.70. what is the probability that a the 5th goal is made on the players 8th shot? what is the expected value of the probability?

pro4ph5e4q2 2021-11-15

Two coins are tossed.
a. Find the probability that both are heads
b. Find the probability that one is heads and one is tails.
c. Find the probability that both are tails.
d. Which is more likely: that the two coins match or that they don’t match? Why?

klytamnestra9a 2021-11-15

Suppose that a family has 5 children. Also, suppose that the probability of having a boy is 12.
Find the probability that the family has at least 4 boys.
The probability that the family has at least 4 boys is?

gamomaniea1 2021-11-15

Teams A and B are in a five-game playoff matchup; the team that wins three games is the team that wins the series. Assuming that both teams are evenly matched (i.e., the probability of winning each game is 50/50).
(a) Team A won the first game. What is the probability that team B will win the series?
(b) Continue to assume that Team A has already won one game, but the teams are not evenly matched. Assume that B is a better team. It’s better in that its probability of beating Team A in any one game is .55. What is the probability that Team B will win the series?

ikavumacj 2021-11-15

You are expecting two sets of exams- “easy” and “hard”. The probability of getting a hard exam is 0.80. The probability that the first question on the exam will be difficult is 0.90 if the set is “hard” and is 0.15 if the set is “easy.
a) What is the probability that the first question on your exam is marked as difficult.
b) What is the probability that your exam is hard given that the first question on the exam is marked as difficult?

ZIHLOLEp3 2021-11-15

The accompanying table gives information on the type of coffee selected by someone purchasing a single cup at a particular airport.
Small Medium Large
Regular Coffee 14% 20% 26%
Black Coffee 20% 10% 10%
Consider randomly selecting such a coffee purchaser.
a. What is the probability that the individual purchased a small cup?
b. What is the probability that the individual purchased a cup of black coffee?
c. If we learn that the selected individual purchased a small cup, what now is the probability that he/she chose black coffee, and how would you interpret this probability?
d. If we learn that the selected individual purchased black coffee, what now is the probability that a small size was selected?

Cordazzoyn 2021-11-15

Do you have any idea about conditional probability?
Formulate a mathematical problem to explain conditional probability?

danrussekme 2021-11-15

From past experience, Anna knows that the probability that her friend will take her to dinner in Oro Resto is 0.7, the probability that they will watch movies is 0.5, and the probability that he will take her to dinner or they will watch movies is 0.9. What is the probability that
a) They will do both?
b) They will do neither?

korporasidn 2021-11-15

A company’s revenue is considerably below expectation with probability 0.08, is slightly below expectation with probability 0.19, exactly meets expectation with probability 0.26, is slightly above expectation with probability 0.36, and is considerably above expectation with probability 0.11. Let A be the event that the revenue is not below expectation. Let B be the event that the revenue is not above expectation. FIND the probability of the intersection and union of these two events?

deliredejoker7m 2021-11-14

The probability that a regularly scheduled flight departs on time is $P (D) = 0.83$ , the probability that it arrives on time is $P (A) = 0.82$ ; and the probability that it departs and arrives on time is $P (D \cap A) = 0.78$ . Find the probability that a plane:
a. arrives on time given that it departed on time
b. departed on time given that it has arrived on time

alka8q7 2021-11-14

At a particular factory, refrigerators inspectors on an assembly line notice that a randomly selected refrigerator will have too much enamel with probability 0.2, too little enamel with probability 0.25, uneven application with probability 0.33, and no defects with probability 0.43. Note that it is not possible for the same refrigerator to have both too much and too little enamel. Draw the Venn diagram (but do not complete it) before answering the following questions:
(a) What is the probability that a randomly selected refrigerator has a paint defect (i.e. either too much enamel, too little enamel, or uneven application)?
(b) What is the probability of a paint defect from an improper amount of paint (i.e. too much or too little enamel)?
(c) What is the probability of a paint defect resulting from uneven application but not from an improper amount of paint?

ambiguit 2021-11-14

What is the probability of each of the following events:
1) What is the probability that a fair coin lands heads exactly 15 times out of 18 flips?
2) If a biased coin has a probability of heads that is twice the probability of tails and is flipped 100 times, what is the probability of exactly ten heads?

Tomasettiq3 2021-11-14

A specific article is produced by machines $M_{1}, M_{2}, M_{3} and M_{4}$ . The probability that a random article is produced by $M_{1}, M_{2} and M_{3}$ is 0.2, 0.3 and 0.1 respectively, The probability for each machine to produce defective articles is given as $M_{1} = 0.03, M_{2} = 0.02, M_{3} = 0.04 and M_{4} = 0.01$ . What is the probability that a random article was by $M_{4}$ , given that it is non-defective?

xcl3411 2021-11-14

A. The odds in favor of an event are given. Compute the probability of the event. (Enter the probability as a fraction.) 2 to 9
B. The probability of an event is given. Find the odds in favor of the event. 0.3
C. The probability of an event is given. Find the odds in favor of the event. 0.35

ffortunyu 2021-11-14

Our original information was that the probability of Average Sales was .6. We collected the following new information about what happened to sales when there was an improving or not improving economy. Answer the below question.
Calculate the probability for low Sales and the improving economy (also called Joint Probability)?
$\begin{array}{cc} Improving Economy & Not improving economy \\ Given average sales & 0.7 \\ Given low sales & 0.51 \end{array}$
Answer format: Number: Round to: 2 decimal places.

ffortunyu 2021-11-14

On a school night, the probability that a student watches television is 0.71. On a school night, the probability that a student watches television or does their homework is 0.84. On a school night, the probability that they watch television and does their homework is 0.68. On a school night, the probability, to the nearest hundredth, that the student will do homework is:

Maggenifh 2021-11-14

Two firms V and W consider bidding on a road-building job, which may or may not be awarded depending on the amounts of the bids. Firm V submits a bid and the probability is 0.8 that it will get the job provided firm W does not bid. The probability is 0.7 that W will be bid, and if it does, the probability that V will get the job is only 0.4
a) What is the probability that V will get the job?
b) If V gets the job, what is the probability that W did not bid?

If you are looking for high school probability equations, you are in the right place because we can provide you with the list of answers and questions that will help you as you deal with your equations or just need practical examples. If you need to deal with something specific, browse through the list of examples and see how each answer has been handled.

The high school probability differs from those engineering tasks, yet it is not always much simpler if you do not know the basics. Therefore, take your time to see our examples and learn.

High school probability

Probability Examples and Explanations