Probability Equations Explained with Examples

A boat on the ocean is 4 mi from the nearest point on a straight shoreline; that point is 6 mi from a restaurant on the shore. A woman plans to row the boat straight to a point on the shore and then walk along the shore to the restaurant. a. If she walks at 3 mi/hr and rows at 2 mi/hr, at which point on the shore should she land to minimize the total travel time?
b. If she walks at 3 mi/hr, what is the minimum speed at which she must row so that the quickest way to the restaurant is to row directly (with no walking)?

ahgan3j 2021-11-19

Although it’s hard to be definitive in classifying people as right- or left-handed, some studies suggest that about 14% of people are left-handed. Since $0.14 \times 0.14 = 0.0196$ the Multiplication Rule might suggest that there’s about a 2% chance that a brother and a sister are both lefties. What’s wrong with that reasoning?

Pearl Carney 2021-11-19

In a hospital, the probability of male births is 0.4.
a) What is the probability that the number of female births is 9 in the next 20 births?
b) What is the probability that the number of female births is less than 18 in the next 20 births?

kolonelyf4 2021-11-18

Suppose that 30% of all South African workers have permanent employment contracts, while 50% of South African workers have medium-term employment contracts, and the rest have short-term employment contracts. If a worker has a permanent employment contract, the probability is 0.8 that she is a trade union member. Moreover, if a worker has a medium-term employment contract, the probability is 0.4 that she is a trade union member. Finally, if a worker has a short-term employment contract, the probability is 0.2 that she is a trade union member. Using Bayes theorem, the probability that a worker has a permanent contract, given that she is a member of a trade union is . (Note: write your final answers to 3 decimal places).

varaderiyw 2021-11-18

There are 3.5 commercial airliner aircraft crashes on average each month around the world. What is the likelihood that (a) there will be at least two of these accidents in the upcoming month; (b) there will only be one accident in the upcoming month? Describe your thinking!

Douglas Kraatz 2021-11-18

Asconting to a recent national Gallup Pell of U.S. smartphone users, $57 %$ upgrede their cell phone every two years.
Use this information to answer the following questions. Show all work. Be sure to include your probability and calculator statements for the questions where indicated.
Determine the probability (to 4 decimal places) that:
A. exactly 8 users out of 15 smartphone users do not upgrade their cell phones every two years.
Probability statement:
[State question using probability notation:P( )]
Calculator Function w/values:
[List TI calculator function with values used to solve this problem.]
B. at most 7 users of 15 smartphone users upgrade their cell phones every 2 yeas.
Probability statement:
[State question using probability notation: P( )]
Calculator Function w/values:
[List TI calculator function with values used to solve this problem.]
C. between 10 and 12 users, inclusive, of the 15 smartphone users do not upgrade their cell phones every two years.
Probability statement:
[State question using probability notation: P( )]
Calculator Function w/values:
[List TI calculator function with values used to solve this problem.]

Coroware 2021-11-18

Formulate a mathematical problem to explain conditional probability.

Serotoninl7 2021-11-18

50 Students in the 1-st class, 15 of them failed in mathematics, 10 of them failed in mechanics and 10 failed in both, if a random is selected, find?
1. Probability that fail in mathematics and succed in mechanics
2. Probability that fail in machanics and succeed in mathematics
3. Probability that fail in one of them at least

akutagawatj 2021-11-18

Giving a test to a group of students, the grades and gender are summarized below
$\begin{array}{cc} A & B & C & T o t a l \\ M a l e & 7 & 16 & 19 & 42 \\ F e m a l e & 10 & 3 & 18 & 31 \\ T o t a l & 17 & 19 & 37 & 73 \end{array}$
If one student is chosen at random,
Find the probability that the student got a C:
Find the probability that the student was male AND got a "C":
Find the probability that the student was male OR got an "A":
If one student is chosen at random, find the probability that the student got a C GIVEN they are male:

Ann Tice 2021-11-18

Assume the number of commuters using the QR code payment service at each MTR station follows a Poisson probability distribution. Based on a recent statistics, on average, 3 commuters use the QR code payment service in an hour.
(i) What is the probability there are exactly 10 commuters who use the QR code payment service in an hour?
(ii) What is the probability that there are less than 4 commuters who use the QR code payment service in 3 hours?
(iii) If five MTR stations are randomly selected, what is the probability that at least two of the five MTR stations will have less than 4 commuters who use the QR code payment service in 3 hours?

scottyqegi 2021-11-18

2 Producers (A and B) supply car mirrors to Distributor. If mirror is picked up at random, Probability that it is from A is 0.25, from B - 0.75. Due to manufacturer’s failure, some mirrors are defected. Probability that mirror by A is defected is 0.04. Probability that mirror by B is defected is 0.02. Find out the probability that mirror selected at random will be defected.

rescuedbyhimw0 2021-11-18

A die is weighted in such a way that each of 2, 4, and 6 is twice as likely to come up as each of 1, 3, and 5. Find the probability distribution and find the probability of rolling less than 3.
$\begin{array}{cc} O u t c o m e & 1 & 2 & 3 & 4 & 5 & 6 \\ P r o b a b i l i t y \end{array}$

Boduszewox6 2021-11-18

A radar center consists of two units operating independently. The probability that one of the units detects an incoming missile is 0.99, and the probability that the other unit detects it is 0.95. What is the probability that
(i) both units will detect?
(ii) at least one will detect?
(iii) neither will detect?

Cordazzoyn 2021-11-18

Different hands are possible while playing 7-card poker with a conventional 52-card deck, 52C7, or 133,784,560. The likelihood of receiving different hands is calculated by dividing the total number of possible outcomes by 133,784,560. The probabilities and number of possible outcomes for each type of hand are displayed to the right. Calculate the likelihood of not receiving this kind of hand.
$\begin{array}{cc} Number of ways the hand can occur & p r o b a b i l i t y \\ 7480 & 7480 / 133, 784, 560 \end{array}$

aidmoong7 2021-11-18

You randomly select one card from a standard deck.
(a) What is the probability of selecting a king or a queen?
(b) What is the probability of selecting a face card or a 10?
(c) What is the probability of selecting a spade or a heart?
(d) What is the probability of selecting a red card or a black card?

gainejavima 2021-11-18

The probability that an automobile being filled with gasoline also needs an oil change is 0.25; the probability that it needs a new oil filter is 0.40; and the probability that both the oil and the filter need changing is 0.14.
(a) If the oil has to be changed, what is the probability that a new oil filter is needed?
(b) If a new oil filter is needed, what is the probability that the oil has to be changed?

deliredejoker7m 2021-11-18

(a) The probability that an automobile being filled with gasoline will also need an oil change is 0.35; the probability that it needs a new oil filter is 0.45; and the probability that both the oil and filter need changing is 0.25.
(i) If the oil had to be changed, what is the probability that a new oil filter is needed ?
(ii) If a new oil filter is needed, what is the probability that the oil has to be changed ?

Agaiepsh 2021-11-17

Butch has a collection of 70 vinyl records from throughout the 20th century including nine from the 40s, four from the 50s, nine from the 60s, seven from the 70s, and 14 from the 80s. If he randomly selects one from his collection of 70, find the probability it will be from each of the following decades.
The probability that itis from the 40s is,
The probability that itis from the 50s is,
The probability that itis from the 60s is,
The probability that itis from the 70s is,
The probability that itis from the 80s is,

signokodo7h 2021-11-17

The probability that a person selected at random from a population will exhibit the classic of a centrain disease is 2, and the probability that a person selected at random has the disease is 23. The probability that a person who has the symptom also has the disease is 18. A person selected at random from the population does not not have the symptom.
What is the probability that the person has the disease?

sputavanomr 2021-11-17

A file contains 1Kbytes (i.e. 1000 bytes). The probability that there exists at least one corrupted byte is 0.01. The probability that at least two bytes are corrupted is 0.005. Let the outcome of the experiment be the number of bytes in error.
a) Define the sample space.
b) Find the probability of no errors.
c) Find the probability of exactly one byte in error.
d) Find the probability of at the most one byte is in error.

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