M230 Test II Fall 1997Solutions

1. Find
Since there are 6 sides to each of the dice, there are 36 total possible outcomes.
S possibilities
2 (1,1)
3 (2,1) (1,2)
4 (3,1) (2,2) (1,3) So, and
5 (4,1) (3,2) (2,3) (1,4)
6 (5,1) (4,2) (3,3) (2,4) (1,5) So
7 (6,1) (5,2) (4,3) (3,4) (2,5) (1,6)
8 (6,2) (5,3) (4,4) (3,5) (2,6)
9 (6,3) (5,4) (4,5) (3,6)
10(6,4) (5,5) (4,6)
11(6,5) (5,6)
12(6,6)

2. For Bernoulli trials E[X]=np and Var[X]=npq where n = the number of trials, p =the probability of "correct", and q = the probability of "incorrect".

For this problem there are 2 answer choices for each question, one correct and one incorrect. So . There are 10 questions on the quiz, so n = 10.

So, and .

3. (a)Let NA = the event that the asteroids do not get to the game and NC = the event that the comets do not get to the game.

Since the events that the teams get to the ball park are independent, we can say that . The probability that the comets do not get to the game is . The probability that the asteroids do not get to the game .

So, the answer is

(b)

When the comets beat the asteroids, the comets and the asteroids must show up the game and the steroids must win. When the comets win by default, the asteroids must not show up and the comets must show up. So (the event that the comets win by default) = (the event that the comets come to the game) AND (the event that the asteroids do not come to the game). Also, (the event that the comets beat the asteroids) = (the comets come to the game) AND (the asteroids come to the game) AND (the comets win).

So, the answer is

(c) Let C = the event that the comets won the game
Let NA = the event that the asteroids did not come to the game
Let YC = the event that the comets came to the game

4. n = 7 and