1. Let the sample space represent all the values from 1 to 10. Let A = {1, 2, 8} and B = {2, 7}. What is the P(A ∩ B)?
2 answers:
A B denotes to all common elements in both A and B
- Sample space=S={1,2,3,4,5,6,7,8,9,10}
So
- A={1,2,8}
- B={2,7}
2 is common
Hence
A $\cap$ B={2}
Answer:
P(A ∩ B) = 1/10
Step-by-step explanation:
Given:
- Sample space (S) = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
- A = {1, 2, 8}
- B = {2, 7}
We can represent this information in a Venn diagram (see attachment 1).
As there are 10 equally likely outcomes (which must add up to 1), the probability of each outcome is 1/10.
Therefore, we can redraw the Venn diagram with the probabilities instead of the values (see attachment 2).
P(A ∩ B) means the probability of events A and B happening together, so it is the section of the diagram where events A and B overlap.
Therefore, P(A ∩ B) = 1/10
You might be interested in
Answer:
15.24% probability that at least 2 will still stand after 35 years
Step-by-step explanation:
To solve this question, we need to understand the binomial distribution and the exponential distribution.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
Exponential distribution:
The exponential probability distribution, with mean m, is described by the following equation:
In which is the decay parameter.
The probability that x is lower or equal to a is given by:
Which has the following solution:
The probability of finding a value higher than x is:
Probability of a single tower being standing after 35 years:
Single tower, so exponential.
Mean of 25 years, so
We have to find
What is the probability that at least 2 will still stand after 35 years?
Now binomial.
Each tower has a 0.2466 probability of being standing after 35 years, so
3 towers, so
We have to find:
In which
15.24% probability that at least 2 will still stand after 35 years
1. - Cone
2. - Sphere
3. - Cylinder
4. - Pyramid
5. - Prism
Solution:
1.
Lateral surface area of cone =
where r is the radius of the cone and l is the slant height of the cone.
2.
Volume of sphere =
where r is the radius of the sphere.
3.
Total surface area of cylinder =
where r is the radius of the cylinder and h is the height of the cylinder.
4.
Volume of pyramid =
where B is the base area of the pyramid and h is the height of the pyramid.
5.
Lateral surface area of prism =
where p is the perimeter of the base and h is the height of the prism.