Help with Math Homework: Conditional Probability - 19/30

In summary, the conversation is about finding the probability of selecting an afternoon course from either the history or psychology department. The correct answer is 19/30, and the mistake made in getting 13/30 was in adding the fractions. The events A and B represent selecting an afternoon course from the history and psychology departments, respectively.
  • #1
navi
12
0
Hey! I need help with my Math homework :( The question is the following...

There are 5 history courses of interest to Howard, including 3 in the afternoon, and there are 6 psychology courses, including 4 in the afternoon. Howard picks a course by selecting a dept at random, then selecting a course at random. Find the pr that the course he selects is in the afternoon.

The answer is 19/30, but I get 13/30 by doing this:

For the history dept, the probability of an afternoon class is 1/2 x 3/5, or 3/10, and for the psych dept, the pr of an afternoon class is 1/2 x 4/6, or 1/3. I then add 1/3 and 3/10 and I get 13/30, but that is not the answer and I have no idea what I could be doing wrong...

Please help :(
 
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  • #2
Hello, and welcome to MHB! (Wave)

I would let event A be that Howard selected an afternoon course from the history department, and event B be that Howard selected an afternoon course from the psychology department.

\(\displaystyle P(A)=\frac{1}{2}\cdot\frac{3}{5}=\frac{3}{10}\)

\(\displaystyle P(B)=\frac{1}{2}\cdot\frac{4}{6}=\frac{1}{3}\)

And so:

\(\displaystyle P(A\text{ OR }B)=P(A)+P(B)=\frac{3}{10}+\frac{1}{3}=\frac{3\cdot3+10\cdot1}{30}=\frac{19}{30}\)

You just made an error in adding the fractions...your analysis of the problem was good. :)
 
  • #3
MarkFL said:
Hello, and welcome to MHB! (Wave)

I would let event A be that Howard selected an afternoon course from the history department, and event B be that Howard selected an afternoon course from the psychology department.

\(\displaystyle P(A)=\frac{1}{2}\cdot\frac{3}{5}=\frac{3}{10}\)

\(\displaystyle P(B)=\frac{1}{2}\cdot\frac{4}{6}=\frac{1}{3}\)

And so:

\(\displaystyle P(A\text{ OR }B)=P(A)+P(B)=\frac{3}{10}+\frac{1}{3}=\frac{3\cdot3+10\cdot1}{30}=\frac{19}{30}\)

You just made an error in adding the fractions...your analysis of the problem was good. :)
lol I see, thanks!
 

FAQ: Help with Math Homework: Conditional Probability - 19/30

1. What is conditional probability?

Conditional probability is a mathematical concept that measures the likelihood of an event occurring given that another event has already occurred. It is represented by P(A|B), where A is the event we are interested in and B is the event that has already occurred.

2. How do I calculate conditional probability?

To calculate conditional probability, you need to use the following formula: P(A|B) = P(A and B) / P(B). This means that you need to find the probability of both events occurring (A and B) and divide it by the probability of event B occurring on its own.

3. What does the fraction in conditional probability represent?

The fraction in conditional probability represents the ratio of the number of favorable outcomes to the total number of outcomes. In other words, it shows how likely it is for event A to occur given that event B has already occurred.

4. How is conditional probability used in real-life situations?

Conditional probability is commonly used in fields such as statistics, economics, and biology to make predictions and analyze data. It can be applied to real-life situations such as weather forecasting, medical diagnoses, and risk assessment in insurance.

5. What are some common misconceptions about conditional probability?

One common misconception about conditional probability is that it is the same as regular probability. However, regular probability deals with the likelihood of an event occurring on its own, while conditional probability takes into account the occurrence of another event. Another misconception is that conditional probability always increases when an event occurs, but this is not always the case and depends on the specific events and their relationship.

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