High school probability Uncovered: Discover the Secrets with Plainmath's Expert Help

Suppose our experiments consist ofrolling a six-sided die. Then we can define the appropriate sample space as ${\displaystyle S=\{1,2,3,4,5,6\}}$.
I.What is probability that we roll a 2?
II.What is probability that we roll a 2 or 5?
III.What is probability that we roll an even number?

The probability of a student cheating is 0.6, the probability of a student getting caught given that he/she has cheated is 0.3 and the probability of a student not getting caught given that he/she has cheated is 0.7. Lets

The probability that a shopper will buy a PS3 is 0.40.
The probability that a shopper will buy an X-Box 360 is 0.54.
The probability that a shopper will buy a Nintendo DS is 0.30.
The probability that a shopper will buy both a PS3 and an X-Box 360 is 0.13. The probability that a shopper will buy both a PS-3 and a DS is 0.12.
The probability that a shopper will buy both an X-Box 360 and a DS is 0.07. There is no chance that a shopper will buy all three systems.
Find the probability that a random shopper will:
a) Buy only a PS-3
b) Buy exactly one type of system
c) Buy exactly two types of systems d) Not buy any of the three systems

A standard deck of cards contains 52 cards. One card is selected from the deck.
a) Compute the probability of randomly selecting a spade or diamond.
b) Compute the probability of randomly selecting a spade or diamond or heart.
c) Compute the probability of randomly selecting a king or club.
a. ${\displaystyle P\left(\text{spade or diamond}\right)=?}$
b. ${\displaystyle P\left(\text{spade or diamond or heart}\right)=?}$
c. ${\displaystyle P\left(\text{king or club}\right)=?}$

If the probability that it rains on Thursday is 30% and the probability that it rains on Sunday is 20%, what is the probability that it does not rain on both days?

A machine contains 10 processors that operate independently. The probability that a processor fails is 0.08
(a) What is the probability that exactly 4 of the processors fail?
(b) What is the probability that at most 1 of the processors fails

In a class, the probability that a student owns a laptop is 0.2. Find the probability that the 5-th student to be interviewed owns a laptop.

Consider in the 1st class of civil engineering department, 15% of students fail in mechanics, 10% of students fail in mathematics, and 7% of students fail in both. If a random student is selected, find:
1) Probability if he is good in mechanics to be bad in mathematics.
2) Probability if he is bad in mathematics to be bad in mechanics.
3) Probability if he is good in mathematics to be bad in mechanics.

Tony and Sam play chess (either of them wins, draw is not allowed). If Tony plays White, probability of him winning is 0.72. If Tony plays Black, probability of him winning is 0.63. Tony and Sam play 2 games and in second game they change sides. Find the probability that Sam wins both games.

The probability of event ${\displaystyle A^c}$ is 0.4, the probability of ${\displaystyle {\left(AUB\right)}^c}$ is 0.1, and the probability of the intersection of Aand Bis.2. Whats the probability of event 8?

Assume that the business makes a profit with probability 0.4 in the first year. For each year thereafter, the business makes a profit with probability 0.6 if it made a profit in the previous year, and with probability 0.4 if it did not make a profit in the previous year.
What is the probability that the business makes a profit in exactly two of its first three years?

In shooting arena there are 5 different guns. Probability of hitting aim from gun1 is 0.5.
Probability of hitting aim from gun2 is 0.55. Probability of hitting aim from gun3 is 0.7.
Probability of hitting aim from gun4 is 0.75. Probability of hitting aim from gun5 is 0.4. One shoot was made from a gun selected at random. What is the probability that aim was hit?

Given the probability that "she's up all night 'til the sun" OR "she's up all night for good fun" is 0.31, the probability that "she's up all night for good fun" is 0.49, and the probability that "she's up all night 'til the sun" AND "she's up all night for good fun" is 0.39, what's the probability that "she's up all night 'til the sun"?

The table shows the results of a survey of 100 authors by a publishing company.
$$\begin{array}{|cccc|}\hline & \text{New Authors}& \text{Established Authors}& Total\\ Successful& 15& 30& 45\\ Unsuccessful& 20& 35& 55\\ Total& 35& 65& 100\\ \hline\end{array}$$
Compute the following conditional probability. (Enter your probability as a fraction.)
An author is established, given that he is unsuccessful.

Two cards are drawn without replacement from an ordinary​ deck, find the probability that the second is a face card​, given that the first is not a face card.
What is the conditional​ probability?
nothing ​(Type an integer or a simplified​ fraction.)
The Motor Vehicle Department has found that the probability of a person passing the test for a​ drivers

The probability of someone getting covid positive is 0.6, the probability of someone dying suddenly given that
he/she is covid positive is 0.3 and the probability of someone dying suddenly given that he/she is not covid
positive is 0.1. Lets

A Geiger counter counts the number of alpha particles from radioactive material. Over a long period of time, an average of 15 particles per minute occurs. Assume the arrival of particles at the counter follows a Poisson distribution.
a) Find the probability of exactly 20 particles arrive in a particular one minute period.
b) Find the probability of exactly one particle arrives in a particular one second period.
c) Find the probability that at least one particle arrives in a particular one second period.
d) Find the probability that at least two particles arrive in a particular 4 second period.

The probability that a regulary seheduted flightdeparts on time is 0.83 ,
the probability that it arrives on time is 0.92 and the probability that it departs
and arrives on time is 0.78 . Find the probability thata plane
(1) arrives on time given thatit departed on time .
(2) departed on time given that it has arrived on time .