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3 years ago

A and B are independent events. P(A) = 0.50 P(B) = 0.30 What is P(A/B)? a. not enough information. b. 0.30 c. 0.50 d. 0.15

Mathematics

1 answer:

Gala2k [10]3 years ago

3 0

Answer:

0.50

Step-by-step explanation:

P(A|B)=P(A and B)/P(B) is the formula to find a conditional probability when A and B are not independent.

A and B are independent. This means B has no effect of A. This means P(A|B)=P(A).

P(A|B)=P(A) since A and B are independent

P(A|B)=0.50

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3 years ago

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Two types of defects are observed in the production of integrated circuit boards. It is estimated that 6% of the boards have sol

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Answer:

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(b) 0.06

(d) 0.9118

(e) 0.03

Step-by-step explanation:

Let A = boards have solder defects and B = boards have surface defects.

The proportion of boards having solder defects is, P (A) = 0.06.

The proportion of boards having surface-finish defects is, P (B) = 0.03.

It is provided that the events A and B are independent, i.e.

$P(A\cap B)=P(A)\times P(B)$

(a)

Compute the probability that either a solder defect or a surface-finish defect or both are found as follows:

= P (A or B) + P (A and B)

$=P(A)+P(B)-P(A\cap B)+P(A\cap B)\\=P(A)+P(B)\\=0.06+0.03\\=0.09$

Thus, the probability that either a solder defect or a surface-finish defect or both are found is 0.09.

(b)

The probability that a solder defect is found is 0.06.

(c)

The probability that both defect are found is:

$P(A\cap B)=P(A)\times P(B)\\=0.06\times0.03\\=0.0018$

Thus, the probability that both defect are found is 0.0018.

(d)

The probability that none of the defect is found is:

$P(A^{c}\cup B^{c})=1-P(A\cup B)\\=1-P(A)-P(B)+P(A\cap B)\\=1-P(A)-P(B)+[P(A)\times P(B)]\\=1-0.06-0.03+(0.06\times0.03)\\=0.9118$

Thus, the probability that none of the defect is found is 0.9118.

(e)

The probability that the defect found is a surface finish is 0.03.

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