Introduction to negative binomial probability distribution:
Negative binomial distribution is one of the probability distribution types. Pascal distribution is also called as negative binomial distribution. The distribution of the probability negative variable is called as negative binomial distribution. In negative distribution we are conducting a negative experiment. In this article we shall discuss negative binomial probability distribution example problems.
Negative Binomial Probability Distribution Example Problem
Example:
A coin is flipped; find the probability of flipping a coin gets the fifth tail on the tenth flip.
Solution:
Step 1:
Here,
Total number of trials n = 10 (flipping the coin ten times).
Number of successes r = 5 (tail as a success).
Probability of success for any coin flip p = 0.5
Step 2:
Find n-1 and r-1.
n-1 = 10-1 = 9
r-1 =5-1 = 4
Step 3:
To find n-1Cr-1 Calculate ((n-1)-(r-1))!
(n-1)-(r-1) = 9-4 = 5
((n-1)-(r-1))! = 5! = 120.
Step 4: Find (n-1)!
= 9! = 362880
Step 5: Find (r-1)!
= 4! = 24.
Step 6: Find (n-1)! / ((n-1)-(r-1))!
= 362880/120 = 3024
Step 7: To solve n-1Cr-1 formula.
= 3024/24 = 126
Step 8: Find pr.
= 0.55 = 0.03125
Step 9: To Find (1-p)n-r Calculate 1-p and n-r.
1-p = 1-0.5 = 0.5
n-r = 10-5 = 5
Step 10: Calculate (1-p)n-r.
= 0.55 = 0.03125
Step 11: Calculate Negative Binomial Distribution.
= 126×0. 03125 ×0.03125 = 0.12304675.
The probability on tails for the fifth time on the tenth coin flip is 0. 1230.
Example:
A coin is flipped; find the probability of flipping a coin gets the sixth tail on the twelfth flip.
Solution:
Step 1:
Here,
Total number of trials n = 12 (flipping the coin towel times).
Number of successes r = 6 (tail as a success).
Probability of success for any coin flip p = 0.5
Step 2:
Find n-1 and r-1.
n-1 = 12-1 = 11
r-1 =6-1 = 5
Step 3:
To find n-1Cr-1 Calculate ((n-1)-(r-1))!
(n-1)-(r-1) = 11-5 = 6
((n-1)-(r-1))! = 6! = 720.
Step 4: Find (n-1)!
= 11! = 39916800
Step 5: Find (r-1)!
= 5! = 120.
Step 6: Find (n-1)! / ((n-1)-(r-1))!
= 39916800 /120 = 55440
Step 7: To solve n-1Cr-1 formula.
= 55440 /120 = 462
Step 8: Find pr.
= 0.56 = 0.015625
Step 9: To Find (1-p)n-r Calculate 1-p and n-r.
1-p = 1-0.5 = 0.5
n-r = 12-6 = 6
Step 10: Calculate (1-p)n-r.
= 0.56 = 0.015625
Step 11: Calculate Negative Binomial Distribution.
= 462 ×0. 015625×0. 015625= 0.1127929875.
The probability on tails for the sixth time on the twelfth coin flip is 0. 11279.I have recently faced lot of problem while learning how to simplify rational expressions, But thank to online resources of math which helped me to learn myself easily on net.
Negative Binomial Probability Distribution Practice Problem
Problem:
A coin is flipped; find the probability of flipping a coin gets the seventh head on the tenth flip
Answer:
The probability on heads for the fifth time on the tenth coin flip is 0. 0.08203.
Problem:
A coin is flipped; find the probability of flipping a coin gets the fourth tail on the eight flip
Answer:
The probability on tails for the fifth time on the tenth coin flip is 0. 0.13672.
Negative binomial distribution is one of the probability distribution types. Pascal distribution is also called as negative binomial distribution. The distribution of the probability negative variable is called as negative binomial distribution. In negative distribution we are conducting a negative experiment. In this article we shall discuss negative binomial probability distribution example problems.
Negative Binomial Probability Distribution Example Problem
Example:
A coin is flipped; find the probability of flipping a coin gets the fifth tail on the tenth flip.
Solution:
Step 1:
Here,
Total number of trials n = 10 (flipping the coin ten times).
Number of successes r = 5 (tail as a success).
Probability of success for any coin flip p = 0.5
Step 2:
Find n-1 and r-1.
n-1 = 10-1 = 9
r-1 =5-1 = 4
Step 3:
To find n-1Cr-1 Calculate ((n-1)-(r-1))!
(n-1)-(r-1) = 9-4 = 5
((n-1)-(r-1))! = 5! = 120.
Step 4: Find (n-1)!
= 9! = 362880
Step 5: Find (r-1)!
= 4! = 24.
Step 6: Find (n-1)! / ((n-1)-(r-1))!
= 362880/120 = 3024
Step 7: To solve n-1Cr-1 formula.
= 3024/24 = 126
Step 8: Find pr.
= 0.55 = 0.03125
Step 9: To Find (1-p)n-r Calculate 1-p and n-r.
1-p = 1-0.5 = 0.5
n-r = 10-5 = 5
Step 10: Calculate (1-p)n-r.
= 0.55 = 0.03125
Step 11: Calculate Negative Binomial Distribution.
= 126×0. 03125 ×0.03125 = 0.12304675.
The probability on tails for the fifth time on the tenth coin flip is 0. 1230.
Example:
A coin is flipped; find the probability of flipping a coin gets the sixth tail on the twelfth flip.
Solution:
Step 1:
Here,
Total number of trials n = 12 (flipping the coin towel times).
Number of successes r = 6 (tail as a success).
Probability of success for any coin flip p = 0.5
Step 2:
Find n-1 and r-1.
n-1 = 12-1 = 11
r-1 =6-1 = 5
Step 3:
To find n-1Cr-1 Calculate ((n-1)-(r-1))!
(n-1)-(r-1) = 11-5 = 6
((n-1)-(r-1))! = 6! = 720.
Step 4: Find (n-1)!
= 11! = 39916800
Step 5: Find (r-1)!
= 5! = 120.
Step 6: Find (n-1)! / ((n-1)-(r-1))!
= 39916800 /120 = 55440
Step 7: To solve n-1Cr-1 formula.
= 55440 /120 = 462
Step 8: Find pr.
= 0.56 = 0.015625
Step 9: To Find (1-p)n-r Calculate 1-p and n-r.
1-p = 1-0.5 = 0.5
n-r = 12-6 = 6
Step 10: Calculate (1-p)n-r.
= 0.56 = 0.015625
Step 11: Calculate Negative Binomial Distribution.
= 462 ×0. 015625×0. 015625= 0.1127929875.
The probability on tails for the sixth time on the twelfth coin flip is 0. 11279.I have recently faced lot of problem while learning how to simplify rational expressions, But thank to online resources of math which helped me to learn myself easily on net.
Negative Binomial Probability Distribution Practice Problem
Problem:
A coin is flipped; find the probability of flipping a coin gets the seventh head on the tenth flip
Answer:
The probability on heads for the fifth time on the tenth coin flip is 0. 0.08203.
Problem:
A coin is flipped; find the probability of flipping a coin gets the fourth tail on the eight flip
Answer:
The probability on tails for the fifth time on the tenth coin flip is 0. 0.13672.
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