3. Suppose we consider the following two step experiment: Step1: we roll a fair 3-sided die with labels - 1, 2, 3 two times. Step 2: If the sum of the two rolls in Step1 is even we toss a fair coin with P(H) = 0.5 Else we toss a coin with P(H) = 0.8 Let E = Sum of the two rolls is less than or equal to 3 and F: (a) Draw the labelled tree diagram for this experiment. (b) List out the outcomes in the events E, F, and En F. (c) Calculate P(E), P(F), P(G), P(E|F) (d) Are E and F independent? = Coin lands H.

4) Flue cases per school this past flu season in the Remulak school system (n = 500) were 15 per week. For the entire state, the weekly average was 16 (SD = 15.1). Are the kids in Remulak as sick as the kids throughout the state?

Given X and Y are two events. LetP(M)= 0.49, P(N) = 0.44, P(MN) = 0.17 Find the value of P(M/N'),given M and N are two events.

llustration 19.18.. A sample study of the population of two districts gives that in district A the percentage of male population is 52% while this is the figure for the female percentage in the B district. If the size of the sample selected was in district A and B as 400 and 625 respectively, can both of these samples be taken to come from a population where the percentage of males and females is equal?

Consider the experiment of rolling 3 fair four-sided dice (the numbers on each die are 1,2,3 and 4). X 1, X 2 and X 3 denote the numbers on the first, second, and third die, respectively. Y = X 1+X_2+X_3, the sum of the three rolls. What is E(X_2]Y)? 3.5 O 2.5 OY/2 Y/3 Ox2 X_2

2. A random variable X has only two values a and b with P(X = a) = p , P(X = b) = q (p+ q = 1). Find its mean value and variation.

The accompanying diagram represents a two-stage experiment. Here,  B = (A ∪ C)c.  Complete the information on the diagram, and use it to find the following.   (a)     P(D) (b)     P(B | D) (c)     P(Dc) (d)     P(A | Dc)

1. In Hawaii, January is a favorite month for surfing since 60% of the days have a surf of at least 6 feet high. You pick 7 random days to go surfing in January. Let r be the number of days that the surf reaches 6 feet high. Read the problem carefully and answer the following questions: (a) n = 7 (b) What is p (in decimal form) = ,le %3D (c) What is q (in decimal form) = 94 %3D (d) Fill in the table by using the Binomial Distribution table P(r) .002 •017 .077 .194 .290 . 261 6. .131 •028 (e) What is the probability of getting 5 or more days when the surf is at least 6 feet high? 261 0131 .028 0672 l67.27 (f) What is the probability of getting fewer than 3 days when the surf is at least 6 feet high? 077 cala a let- 이 2 • 01 7 9.167- •002 (g) What is the expected number of days when the surf will be at least 6 feet? Calculate u (h) What is the standard deviation? (i) Use Microsoft excels to create a bar graph of the probability distribution. Use the tables value in part (d) and the steps…

If p (E1) = 0.3, p (E2) = 0.4 p(E1/E2)=0.5 so p(E1 cross E2)= 0.2 0.15 0.12 0.7 %3D

A fair 6-sided die is tossed. If X denotes the random variable giving the number on the bottom face of the die, find E(X).E(X) =