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Ahat [919]
2 years ago
7

Samples of emissions from three suppliers are classified for conformance to air-quality specifications. The results from 100 sam

ples are summarized as follows:
conforms
yes no
1 22 8
supplier 2 25 5
3 30 10

Let A denote the event that a sample is from supplier 1, and let B denote the event that a sample from any supplier conforms to specifications. If a disk is selected at random, determine the following probabilities.

a. P(A)=0.3
b. P(B)=0.77
c. P(A ∩ B) =0.22
d. P(A U B)=0.85
Mathematics
1 answer:
Vlad [161]2 years ago
7 0

Answer

P(A) = 0.30

P(B) = 0.77

P(A\ n\ B) = 0.22

P(A\ u\ B) = 0.85

Explanation:

Given

See attachment for proper data presentation

n = 100 --- Sample

A = Supplier 1

B = Conforms to specification

Solving (a): P(A)

Here, we only consider data in sample 1 row.

Here:

Yes = 22 and No = 8

n(A) = Yes + No

n(A) = 22 + 8

n(A) = 30

P(A) is then calculated as:

P(A) = \frac{n(A)}{Sample}

P(A) = \frac{30}{100}

P(A) = 0.30

Solving (b): P(B)

We only consider data in the Yes column.

Here:

(1) = 22    (2) = 25 and (3) = 30

n(B) = (1) + (2) + (3)

n(B) = 22 + 25 + 30

n(B) = 77

P(B) is then calculated as:

P(B) = \frac{n(B)}{Sample}

P(B) = \frac{77}{100}

P(B) = 0.77

Solving (c): P(A n B)

Here, we only consider the similar cell in the yes column and sample 1 row.

i.e. [Supplier 1][Yes]

This is represented as: n(A n B)

n(A\ n\ B) = 22

The probability is then calculated as:

P(A\ n\ B) = \frac{n(A\ n\ B)}{Sample}

P(A\ n\ B) = \frac{22}{100}

P(A\ n\ B) = 0.22

Solving (d): P(A u B)

This is calculated as:

P(A\ u\ B) = P(A) + P(B) - P(A\ n\ B)

This gives:

P(A\ u\ B) = \frac{30}{100} + \frac{77}{100} - \frac{22}{100}

Take LCM

P(A\ u\ B) = \frac{30+77-22}{100}

P(A\ u\ B) = \frac{85}{100}

P(A\ u\ B) = 0.85

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