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## Precalculus

### Unit 8: Lesson 1

Venn diagrams and the addition rule

AP.STATS:
VAR‑4 (EU)
,
VAR‑4.C (LO)
,
VAR‑4.C.2 (EK)
,
VAR‑4.E (LO)
,
VAR‑4.E.4 (EK)
CCSS.Math:
Venn diagrams and the addition rule for probability. Created by Sal Khan.

## Want to join the conversation?

• Hello everyone! I hope this question is not too hard to answer. I understand why we remove the intersection (5/29), to avoid overestimating the probability. We use 5/29, because this is a given value (we already know that there are 5 yellow cubes). But when we apply the intersection rule [P(yellow)*P(cubes)], we get: 12/29*13/29, which is not equivalent to 5/29. Why is that so? What am I missing here? Thank you! • I take it that by the "intersection rule" you mean the rule which states:

P( A ∩ B ) = P(A) x P(B)

This rule only applies when the two events are independent. This is not always a given. What independence means is that the probability of event B is the same whether or not even A occurred.

In this case, there is (overall) a 12/29 = 0.41 chance of drawing something Yellow. However, if we know that we picked a Cube, the probability that we have something Yellow is no longer 0.41, it's 5/13 = 0.38. Hence, the probability is not constant. So the events are not independent, and we can't just multiply the probabilities to get the intersection.
• why would the probability be zero in case of mutual exclusiveness when you can count the probability that someothing or something else has been taken out of the bag even if they dont overlap? Like if you have green, red and yellow cubes and you ask about the probability of taking out green or red than you can solve that even though they dont overlap. this got me confused. • In your case of green, red and yellow cubes, overlapping would be like asking what is the probability of picking a cube that is red and yellow. That is just not possible, right? So the probability would be 0. I hope this answers your question.
• What if you have three or more groups that may or may not overlap, and you want to calculate P(A or B or C ... n)? • kk so i need help. Let's say i have 27 blueberry pancakes. How many banana pancakes would i need to add to make the probability of grabbing a banana pancake 10%?
(1 vote) • Let 𝑏 be the number of banana pancakes.

Thereby we have a total of 𝑏 + 27 pancakes.

We want the probability of picking a banana pancake to be 10%:
𝑏∕(𝑏 + 27) = 0.1

Multiplying both sides by 𝑏 + 27, we get
𝑏 = 0.1𝑏 + 2.7

Subtracting 0.1𝑏 from both sides, we get
0.9𝑏 = 2.7

Finally, dividing both sides by 0.9, we get
𝑏 = 2.7∕0.9 = 3

So, we need to add 3 banana pancakes.
• • anyone noticed the error @ (12+13)/29-5 !=20/29!
(1 vote) • How can all the possibilities be equally likely ( ), if there are different numbers/colors of cubes/spheres? Am I misunderstanding sth? :( • Sal is talking about the fact that every single object has the same chance of falling out first. So each of the 29 objects could fall out of the bag and every single one of them is equally likely at the start of the experiment. In this case for every single object it would be 1/29. The groups(cubes, yellow,...) on the other hand have, because there are different amounts of them, a different chance of falling out. It's important to remember that even we have grouped these objects by shape and colour, they still are single, and in some sense, unique things with there very own likelihood of falling out. And the likelihood is the same for each of them.
• I am a little confused on the "or" rule for combining probabilities. Here is the problem. I have one die with six sides. If I roll the die 8 times, what is the probability that it will come up a six at least once? Using the "or" rule the formula would be
1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6 = 8/6 or a probability of 133%
Am I applying the "or" rule incorrect? Why?

How does this differ from this example. Say the odds of getting killed in a car accident are 1 death per 100,000 miles driven. Each day I drive 1,000. What is the probability that I will be die in a car accident in 50 days? (50%?) 100 days? (100%?) 200 days (200%)...   