Probability Math
In mathematics, probability means likelihood of the outcome of an event of a particular experiment. The probability of event E is written P(E). Probabilities are occurs always numbers between 0 and 1. The set of all possible outcomes of a particular experiment is referred to as sample space. For example, the probability of getting a tail when tossing a coin is 1/2. Please express your views of this topic Continuous Random Variable by commenting on blog.
Probability Math - Example Problems
Example 1:
25 tokens numbered from 1 to 25, two tokens are drawn simultaneously. Find the probability that:
a) Both the tokens drawn have prime number
b) None of the tokens drawn have a prime number
Solution:
We want to select 2 tokens from 25 tokens.
n(S) = 25C2 = 25! / (2! x 23!)
= (25 x 24) / 2
= 300
a) Let A = Event that both the tokens have prime numbers.
Prime numbers between 1 to 25 are: 2, 3, 5, 7, 11, 13, 17, 19, and 23.
Total Numbers = 9.
We have to select 2 numbers from these 9 numbers.
n(A) = 9C2 = 9! / (2! x 7!)
= (9 x 8) / 2
= 36
P(A) = `(n(A)) / (n(S)) `
=` 36/300 `
= `3/25`
b) Non prime numbers between 1 to 25: 25 - 9 = 16
Let B = Event that both the tokens have non-prime numbers.
Now we have to select 2 numbers, from 16 numbers.
n(B) = 16C2 = 16! / (2! x 14!)
= (16 x 15) / 2
= 120
P(B) = n(B) / n(S)
= 120 / 300
= 2/5
Example 2:
A bag contains 5 mangoes and 5 oranges. Two fruits are taken at random. Find the probability that both will be of the same kind.
Solution:
Let S = Sample space
A = the event of taking 2 mangoes.
B = the event of taking 2 oranges.
(A or B) = The event of taking 2 mangoes or 2 oranges.
i.e. the event of taking 2 fruits of same kind.
n(S) = 10C2 = 10! / (2! x 8!) = 10 x 9 / 2= 45
n(A) = 5C2 = 5! / (2! x 3!)
= 5 x 4 / 2
= 10
n(B) = 5C2 = 5! / (2! x 3!)
= 5 x 4 / 2
= 10
P(A) = n(A) / n(S)
= `10/45`
= `2/9`
P(B) = n(B) / n(S)
= `10/45`
= `2/9`
P(A or B) = P(A) + P(B)
=`2/9+2/9`
= `4 / 9`
P(A or B) = 4/9
I have recently faced lot of problem while learning hard 5th grade math problems, But thank to online resources of math which helped me to learn myself easily on net.
Probability Math - Practice Problems
Problem 1:
10 tokens numbered from 11 to 20, two tokens are drawn simultaneously. Find the probability that both the tokens drawn have prime number
Answer: 2/15
Problem 2:
2 dice are thrown simultaneously. What is the probability of getting an odd number as the sum?
Answer: 1/2
In mathematics, probability means likelihood of the outcome of an event of a particular experiment. The probability of event E is written P(E). Probabilities are occurs always numbers between 0 and 1. The set of all possible outcomes of a particular experiment is referred to as sample space. For example, the probability of getting a tail when tossing a coin is 1/2. Please express your views of this topic Continuous Random Variable by commenting on blog.
Probability Math - Example Problems
Example 1:
25 tokens numbered from 1 to 25, two tokens are drawn simultaneously. Find the probability that:
a) Both the tokens drawn have prime number
b) None of the tokens drawn have a prime number
Solution:
We want to select 2 tokens from 25 tokens.
n(S) = 25C2 = 25! / (2! x 23!)
= (25 x 24) / 2
= 300
a) Let A = Event that both the tokens have prime numbers.
Prime numbers between 1 to 25 are: 2, 3, 5, 7, 11, 13, 17, 19, and 23.
Total Numbers = 9.
We have to select 2 numbers from these 9 numbers.
n(A) = 9C2 = 9! / (2! x 7!)
= (9 x 8) / 2
= 36
P(A) = `(n(A)) / (n(S)) `
=` 36/300 `
= `3/25`
b) Non prime numbers between 1 to 25: 25 - 9 = 16
Let B = Event that both the tokens have non-prime numbers.
Now we have to select 2 numbers, from 16 numbers.
n(B) = 16C2 = 16! / (2! x 14!)
= (16 x 15) / 2
= 120
P(B) = n(B) / n(S)
= 120 / 300
= 2/5
Example 2:
A bag contains 5 mangoes and 5 oranges. Two fruits are taken at random. Find the probability that both will be of the same kind.
Solution:
Let S = Sample space
A = the event of taking 2 mangoes.
B = the event of taking 2 oranges.
(A or B) = The event of taking 2 mangoes or 2 oranges.
i.e. the event of taking 2 fruits of same kind.
n(S) = 10C2 = 10! / (2! x 8!) = 10 x 9 / 2= 45
n(A) = 5C2 = 5! / (2! x 3!)
= 5 x 4 / 2
= 10
n(B) = 5C2 = 5! / (2! x 3!)
= 5 x 4 / 2
= 10
P(A) = n(A) / n(S)
= `10/45`
= `2/9`
P(B) = n(B) / n(S)
= `10/45`
= `2/9`
P(A or B) = P(A) + P(B)
=`2/9+2/9`
= `4 / 9`
P(A or B) = 4/9
I have recently faced lot of problem while learning hard 5th grade math problems, But thank to online resources of math which helped me to learn myself easily on net.
Probability Math - Practice Problems
Problem 1:
10 tokens numbered from 11 to 20, two tokens are drawn simultaneously. Find the probability that both the tokens drawn have prime number
Answer: 2/15
Problem 2:
2 dice are thrown simultaneously. What is the probability of getting an odd number as the sum?
Answer: 1/2
