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3 years ago

10

P(A) = 0.50 P(B)= 0.80 P(A and B) = 0.20 . what is P(B\A)?

2 answers:

yawa3891 [41]3 years ago

6 0

Answer:

0.4

Step-by-step explanation:

Use the formula for conditional probability.

P(B|A) = P(A&B)/P(A) = 0.20/0.50 = 0.4

storchak [24]3 years ago

3 0

Answer: P(B/A) = 0.40.

Step-by-step explanation: For any two events A and B, given that

$P(A)=0.50,~~P(B)=0.80,~~P(A\cap B)=0.20.$

We are to find the conditional probability of happening of event B given event A has already happened.

That is,

$P(B/A)=?$

From the formula for conditional probability, we have

$P(B/A)=\dfrac{P(B\cap A)}{P(A)}\\\\\\\Rightarrow P(B/A)=\dfrac{P(A\cap B)}{P(A)}\\\\\\\Rightarrow P(B/A)=\dfrac{0.20}{0.50}\\\\\\\Rightarrow P(B/A)=0.40.$

Thus, P(B/A) = 0.40.

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9. A large electronic office product contains 2000 electronic components. Assume that the probability that each component operat

Marysya12 [62]

Answer:

97.10% probability that five or more of the original 2000 components fail during the useful life of the product.

Step-by-step explanation:

For each component, there are only two possible outcomes. Either it works correctly, or it does not. The probability of a component falling is independent from other components. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

In this problem we have that:

$n = 2000, p = 1-0.995 = 0.005$

Approximate the probability that five or more of the original 2000 components fail during the useful life of the product.

We know that either less than five compoenents fail, or at least five do. The sum of the probabilities of these events is decimal 1. So

$P(X < 5) + P(X \geq 5) = 1$

We want $P(X \geq 5)$

So

$P(X \geq 5) = 1 - P(X < 5)$

In which

$P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{2000,0}.(0.005)^{0}.(0.995)^{2000} = 0.000044$

$P(X = 1) = C_{2000,1}.(0.005)^{1}.(0.995)^{1999} = 0.000445$

$P(X = 2) = C_{2000,2}.(0.005)^{2}.(0.995)^{1998} = 0.002235$

$P(X = 3) = C_{2000,3}.(0.005)^{3}.(0.995)^{1997} = 0.007480$

$P(X = 4) = C_{2000,4}.(0.005)^{4}.(0.995)^{1996} = 0.018765$

$P(X < 5) = P(X = 0) + `P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.000044 + 0.000445 + 0.002235 + 0.007480 + 0.018765 = 0.0290$

$P(X \geq 5) = 1 - P(X < 5) = 1 - 0.0290 = 0.9710$

97.10% probability that five or more of the original 2000 components fail during the useful life of the product.

4 0

3 years ago

Each cylinder is 12 cm high with a diameter of 8 cm.

ludmilkaskok [199]

Answer:

<h2>Volume = 576cm^3</h2>

Step-by-step explanation:

$h = 12 cm\\d = 8cm\\r =d/2 = 8/2 =4\\V = ?\\V =\pi r^2h\\\\V= 3 \times 4^2\times12\\V = 576 cm^3$

6 0

3 years ago

Albert hikes for 0.35 mile. Use a number line to write 0.35 as a fraction. Then find an equivalent fraction.

finlep [7]

0.35 as a fraction is 35 over 100. An equivalent to this is 7 over 20

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Answer:

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2 years ago

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marysya [2.9K]

Answer:

A. log9 3=x

Step-by-step explanation:

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