For any three events A,B, and D, such that P(D) >0, prove that P(Acup B|D) = P(A|D)+P(B|D)-P(Acap B|D).

the standard six-sides dice are rolled (one green and one red). The number on the green is less than the number in the red. The sum of the two numbers is seven. what is the probability of the event?

Consider the experiment of rolling a pair of dice. Suppose that we are interested in the sum of the face values showing on the dice. a. how many sample points are possible? (hint: use the counting rule for multiple-step experiments.) b. list the sample points. c. What is the probability of obtaining a value of 7? d. What is the probability of obtaining a value of 9 or greater? e. because each roll has six possible even values (2, 4, 6, 8, 10, and 12) and only five possible odd values (3, 5, 7, 9, and 11), the dice should show even values more often than odd values. Do you agree with this statement? Explain. f. What method did you use to assign the probabilities requested

Consider the experiment of rolling a pair of dice. Suppose that we are interested in the sum of the face values showing on the dice. a. how many sample points are possible? (hint: use the counting rule for multiple-step experiments.) b. list the sample points. c. What is the probability of obtaining a value of 7? d. What is the probability of obtaining a value of 9 or greater? e. because each roll has six possible even values (2, 4, 6, 8, 10, and 12) and only five possible odd values (3, 5, 7, 9, and 11), the dice should show even values more often than odd values. Do you agree with this statement? Explain. f. What method did you use to assign the probabilities requested

A bag contains ard no. 1 to 25. Two cards are drawn at random one after another without replacement.  Find the probability that no. on each card is multiple of 7.

Dear someone, 

If i choose 20 cell phone numbers randomly in a population of 37 100 000 cell phone subscribers, how large is the probability that at least two of them during two days in a row (a 48 hour period) will make a call to another person in this group of 20? The actual case involve a call and then an immeditate call back, which should mean that the two subscribers know each other: So the question can maybe be reformulated: How large is the probability in a population ot 37 100 000 that two persons in a random sample of 20 drawn from the 37 100 000 know each other?

Is this enough information to answer the question?  

Best regards, 

D Forslund

2. A commercial jet aircraft has four engines. Each engine has independent reliability of     92% For safe landing, at least 2 engines of an aircraft need to function       
a. Compute the probability that an aircraft can land safely           
b. If the probability of safe landing must be 98.3%  compute the minimum required  reliability of each engine assuming two engines min out of 4 have to function         
c. If the reliability cannot be improved beyond  92% find the minimum number of engines which are required for safe landing, using probability of b above for safe landing          
d. Which is a better approach to safety? Look at answers to b and c above. Having 2 engines more reliable or increasing the number of engines? Discuss in numbered points bem.     

83 households have desktop computers 47 have both desktop and laptop 3 percent have neither .what is the probability that a random choice made a laptop household will be choosen

According to a study published by a group of University
of Massachusetts sociologists, approximately
60% of the Valium users in the state of Massachusetts
first took Valium for psychological problems. Find the
probability that among the next 8 users from this state
who are interviewed,
(a) exactly 3 began taking Valium for psychological
problems;
(b) at least 5 began taking Valium for problems that
were not psychological.

80% of YIC students play video or computer games. Choose 3 students at random. The e probability that at least one of 3 play video or computer game is
0.889
0.216
0.992
0.008

You want to obtain a sample to estimate a population mean age of the incoming fall term transfer students. Based on previous evidence, you believe the population standard deviation is approximately σ=6.5${\displaystyle \sigma =6.5}$. You would like to be 95% confident that your estimate is within 2.3 of the true population mean. How large of a sample size is required

If a bag containing 4 red balls numbered 1,2,3,4 and 3 white balls numbered 5,6,7 . What is the probability that the ball is

1)Red or even 

2)White or even

In a class of 100 students, 30 are in mathematics. Moreover, of the 40 females in the class, 10 are in Mathematics. If a student is selected at random from the class, what is the probability that the student will be a male or be in mathematics?

a business operates a drive in facility. on a randomly selected day, let x be the proportion of the time that the drive in facility is in use and suppose that the probability density function isf(X) $$\begin{gathered} \frac{2}{5}(2x^3+3x), 0\le x\le 3 \\ =0 \end{gathered}$$

A manufacturer of a flu vaccine is concerned about the quality of its flu serum. Batches of serum are processed by three different departments having rejection rates of 0.10, 0.08, and 0.12, respectively. The inspections by the three departments are sequential and independent. (a) What is the probability that a batch of serum survives the first departmental inspection but is rejected by the second department? (b) What is the probability that a batch of serum is rejected by the third department?