0.13 Probability: homework  (Page 3/4)

At De Anza College, 20% of the students take Finite Math, 30% take History, and 5% take both Finite Math and History. If a student is chosen at random, find the following conditional probabilities.

1. He is taking Finite Math given that he is taking History.

2. He is taking History assuming that he is taking Finite Math.

At a college, 60% of the students pass Accounting, 70% pass English, and 30% pass both of these courses. If a student is selected at random, find the following conditional probabilities.

1. He passes Accounting given that he passed English.

2. He passes English assuming that he passed Accounting.

If $P\left(F\right)=\text{.}4$ and $P\left(E\mid F\right)=\text{.}3$ , find $P\left(E\text{ and }F\right)$ .

If $P\left(E\right)=\text{.}3$ , and $P\left(F\right)=\text{.}3$ , and $E$ and $F$ are mutually exclusive, find $P\left(E\mid F\right)$ .

If $P\left(E\right)=\text{.}6$ and $P\left(E\text{ and }F\right)=\text{.}\text{24}$ , find $P\left(F\mid E\right)$ .

If $P\left(E\text{ and }F\right)=\text{.}\text{04}$ and $P\left(E\mid F\right)=\text{.}1$ , find $P\left(F\right)$ .

Is the fact that a person checks out a fiction book independent of the main library?

Find the following.

1. $P\left(E\right)$

2. $P\left(F\right)$

3. $P\left(E\cap F\right)$

4. Are $E$ and $F$ independent?

Find the following.

1. $P\left(F\right)$

2. $P\left(G\right)$

3. $P\left(F\cap G\right)$

4. Are $F$ and $G$ independent?

If $P\left(E\right)=\text{.}6$ , $P\left(F\right)=\text{.}2$ , and $E$ and $F$ are independent, find $P\left(E\text{ and }F\right)$ .

If $P\left(E\right)=\text{.}6$ , $P\left(F\right)=\text{.}2$ , and $E$ and $F$ are independent, find $P\left(E\text{ or }F\right)$ .

If $P\left(E\right)=\text{.}9$ , $P\left(F\mid E\right)=\text{.}\text{36}$ , and $E$ and $F$ are independent, find $P\left(F\right)$ .

If $P\left(E\right)=\text{.}6$ , $P\left(E\text{ or }F\right)=\text{.}\text{08}$ , and $E$ and $F$ are independent, find $P\left(F\right)$ .

In a survey of 100 people, 40 were casual drinkers, and 60 did not drink. Of the ones who drank, 6 had minor headaches. Of the non-drinkers, 9 had minor headaches. Are the events "drinkers" and "had headaches" independent?

It is known that 80% of the people wear seat belts, and 5% of the people quit smoking last year. If 4% of the people who wear seat belts quit smoking, are the events, wearing a seat belt and quitting smoking, independent?

John's probability of passing statistics is 40%, and Linda's probability of passing the same course is 70%. If the two events are independent, find the following probabilities.

1. $P\left(\text{both of them will pass statistics}\right)$

2. $P\left(\text{at least one of them will pass statistics}\right)$