5. A red and a blue die are thrown. Both dice are fair (that is, all sides are equally likely). The events A, B, and C are defined as follows: A: The number on the blue die is 1. B: The sum of the numbers on the two dice is less than 4. C: The sum of the numbers on the two dice is even. а. Calculate the probability of each individual event; that is, p(A), p(B), and p(C). b. What is p(B|A)? с. What is p(C|A)? What is p(C\B)? Consider all pairs of events: A and B, A and C, and B and C. Which pairs of events are independent and which pairs of events are not independent? Justify your answer. d. е.

X 4. A bag of fast-food sandwiches contains two hamburgers, four cheeseburgers, and three chicken burgers. If Wyatt ordered a cheeseburger and a chicken burger, what is the probability that a) the first sandwich selected will be one of his choices? b) neither of the first two sandwiches will be among Wyatt's choices?

A math class consist of 25 students , 14 female and 11 male. Three students are selected at random to participate in a probability experiment. Compute the probability that  a. A male is selected , then two females b.a female is selected, the two males c. Two females are selected, then one male d. Three male are selected  e. Three females are selected

3. Two coins are tossed 700 times, and the results are Two heads: 205 times One head: 325 times No head: 170 times Find the probability of each event to occur? 4. If P(A)-7/13, P(B)-9/13 and P(ANB)-4/13, evaluate P(A/B)? 5. Two dice are rolled, find the probability that the sum of the number of both the dice is: A.Equal to 2 B.Equal to 5 C.Less than 12 6. Let X be the number of Tell in four tosses of a fair coin a) Construct the Probability mass function (pf) of X. b) Find the mean number of Tell and the variance c) Find P(0 2. (i)Determine the corresponding p.d.f. (f(x)). (ii) Determine the constant c. 8. If the range and the smallest value of a set of data are 36.8 and 13.4 respectively, then find the largest value 9.Find the probability of getting at least 5 times head-on tossing an unbiased coin for 6 times by using the binomial distribution