Hello, I'm working on probabilities, and I'm stuck on this question. Thanks!

1 answer:

3 0

The relationship between P(B) and P(B|A) is P(B∣A) = [1 - P(A ∪ B)] / [1 - P(B)] which is determined by the probability formula with the conditional rule.

<h3>What is the Probability formula with the conditional rule?</h3>

When event A has already occurred and the probability of occurrence B is required, then P(B, given A) = P(A and B), P(A, given B). It can be vice versa in the case of event B.

P(B∣A) = P(A∩B)/P(A) ....(i)

We know that P(A ∪ B) = P(A) + P(B) - P(A∩B)

So P(A∩B) = P(A) + P(B) - P(A ∪ B)

∵ P(A) + P(B) = 1 ....(ii) (total probability is always one)

So P(A∩B) = 1 - P(A ∪ B) ....(iii)

Substitute the value of equation (iii) in (i),

P(B∣A) = [1 - P(A ∪ B)] / P(A)

From equation (ii), P(A) = 1 - P(B) plug in the value in above equation

P(B∣A) = [1 - P(A ∪ B)] / [1 - P(B)]

Thus, the relationship between P(B) and P(B|A) is P(B∣A) = [1 - P(A ∪ B)] / [1 - P(B)].

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The cutoff numbers for the number of chocolate chips in acceptable cookies are 16.242 and 27.758

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Problems of normally distributed samples can be solved using the z-score formula.

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$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

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