EXAM II

1) Let $E$ and $F$ be events. Assume $P(E)=.7, P(F)=.7$, and $P( E \bigcap F)=.6$. Find $P ( E \bigcup F)$ .

2) A pair of dice is tossed. What is the probability of getting two twos?

A coin is tossed and then a die is rolled.

3) How many outcomes are there?

4) Write down a valid sample space for this experiment.

5) What is the probability of having thrown a tails and an odd number?

6) Let $E$ and $F$ be independent events. Assume $p(E)=.6$ and $P(F)=.8$. Find $P ( E \bigcap F)$.

7) A coin is tossed 9 times. What is the probability of obtaining at least one tail?

8) If $P(E)=.8$ and $P(E \bigcap F) =.4$ , find $P(F\vert E)$.

9) A sample of 5 balls is to be drawn from a box containing 5 red and 7 white balls. Find the probability that the sample contains 2 red and 3 white balls.

10) If $E$ and $F$ are independent events, and if $P(E)=.6$ and $P(F)=.5$, find $P ( E \bigcup F)$.

11) If $P(E \vert F) =.6$ and $P(F)=.5$ find $P ( E \bigcap F)$.

12) Each person in a class of 24 students is randomly assigned a number between 1 and 20. If six students are selected from the class, what is the probability that they have different numbers?.

A preference pole is taken by questioning voters at random in the Philadelphia.and Pittsburgh areas. The probability that a random voter is from the Pittsburgh area is .4 while from the Philadelphia area is .6. It was found that the probability that a random voter from Pittsburgh was a Democrat was .3, and a Republican was .7. It was also found that the probability that a random voter from Philadelphia was a Democrat was .6 and a Republican was .4.

13) Represent this data as a tree diagram.

14)Find the probability that a random voter is both a Republican and from Pittsburgh.

15)Find the probability that a random voter is a Republican.

17)Find the probability that a random Republican voter is from Pittsburgh.