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# Mathematics - Binomial and Poisson probabilities

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Objective: Calculate binomial and Poisson probabilities.

1) Chapter 5: Problem 5.5 (binomial)
Solve the following problems by using the binomial formula.
a. If n = 4 and p = .10 , find P(x = 3) .
b. If n = 7 and p = .80 , find P(x = 4) .
c. If n = 10 and p = .60 , find P(x &#8805; 7) .
d. If n = 12 and p = .45 , find P(5 &#8804; x &#8804; 7) .

2) Chapter 5: Problem 5.6 (binomial) ...
3) Chapter 5: Problem 5.15 (Poisson)a,b,c,d,e,f ...
4) Chapter 5: Problem 5.16 (Poisson)a,b,c,d,e,f ...

[See the attached Question File.]

https://brainmass.com/math/discrete-math/mathematics-binomial-poisson-probabilities-192268

#### Solution Preview

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5.5 Solve the following problems by using the binomial formula.
a. If n = 4 and p = .10 , find P(x = 3) .
b. If n = 7 and p = .80 , find P(x = 4) .
c. If n = 10 and p = .60 , find P(x ≥ 7) .
d. If n = 12 and p = .45 , find P(5 ≤ x ≤ 7) .

P(n, r) = nCx p^x q^(n - x)
(a) P(4, 3) = 4C3 * 0.1^3 * 0.9^1 = 0.0036
(b) P(7, 4) = 7C4 * 0.8^4 * 0.2^3 = 0.115
(c) P(x ≥ 7) = P(10, 7) + P(10, 8) + P(10, 9) + P(10, 10)
= 10C7 * 0.6^7 * 0.4^3 + 10C8 * 0.6^8 * 0.4^2 + 10C9 * 0.6^9 * 0.4^1 + 10C10 * 0.6^10 * 0.4^0 = 0.382
(d) P(5  x  7) = P(12, 5) + P(12, ...

#### Solution Summary

The expert examines the binomial and Poisson probabilities objective. Neat, step-by-step soltuions are provided for all the questions.

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