If p(a) = 0.3, p(b) = 0.2, and p(a ∩ b) = 0.1, determine the following probabilities: a. p(a′) b. p(a ∪ b) c. p(a′ ∩ b) d. p(a ∩ b′) e. p[(a ∪ b)′] f. p(a′ ∪ b)

Arestaurant gives out a scratch-off card to every customer. the probability that a customer will win a prize from a scratch-off card is 25%. design and conduct a simulation using random numbers to find the experimental probability that a customer will need more than 3 cards in order to win a prize. justify the model for your simulation, and conduct at least 10 trials.

Solve the problem. a student earned grades of c, a, b, and a in four different courses. those courses had these corresponding numbers of credit hours: 4, 5, 1, and 5. the grading system assigns quality points to letter grades as follows: a = 4, b = 3, c = 2, d = 1, and f = 0. compute the grade point average (gpa) and round the result to two decimal places. 3.40 3.50 8.75 2.18

Ineed with angles and the measure of them i have abc a is 65 and b is (3x-10) and c is (2x) find the value of x