Question

The probabilities that stock A will rise in price is 0.41 and that stock B will rise in price is 0.59. Further, if stock B rises in price, the probability that stock A will also rise in price is 0.58. a. What is the probability that at least one of the stocks will rise in price? (Round your answer to 2 decimal places.) b. Are events A and B mutually exclusive? Yes because P(A | B) = P(A). Yes because P(A ∩ B) = 0. No because P(A | B) ≠ P(A). No because P(A ∩ B) ≠ 0. c. Are events A and B independent? Yes because P(A | B) = P(A). Yes because P(A ∩ B) = 0. No because P(A | B) ≠ P(A). No because P(A ∩ B) ≠ 0.

          The probabilities that stock A will rise in price is 0.41 and
that stock B will rise in price is 0.59. Further, if stock B rises
in price, the probability that stock A will also rise in price is
0.58.
a. What is the probability that at least one
of the stocks will rise in price? (Round your answer
to 2 decimal places.) 
b. Are events A and B mutually
exclusive?
Yes because P(A | B)
= P(A).
Yes because P(A ∩ B) =
0.
No because P(A | B)
≠ P(A).
No because P(A ∩ B) ≠
0.
c. Are events A and B independent?
Yes because P(A | B)
= P(A).
Yes because P(A ∩ B) =
0.
No because P(A | B)
≠ P(A).
No because P(A ∩ B) ≠
0.

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Added by Ashley B.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Sheryl Ezze

07/15/2022

Step 1

- The probability that stock A will rise in price is 0.41 (P(A) = 0.41). - The probability that stock B will rise in price is 0.59 (P(B) = 0.59). - The probability that stock A will rise in price given that stock B has risen in price is 0.58 (P(A|B) = 0.58). Show more…

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The probabilities that stock A will rise in price is 0.41 and that stock B will rise in price is 0.59. Further, if stock B rises in price, the probability that stock A will also rise in price is 0.58. a. What is the probability that at least one of the stocks will rise in price? (Round your answer to 2 decimal places.) b. Are events A and B mutually exclusive? Yes because P(A | B) = P(A). Yes because P(A ∩ B) = 0. No because P(A | B) ≠ P(A). No because P(A ∩ B) ≠ 0. c. Are events A and B independent? Yes because P(A | B) = P(A). Yes because P(A ∩ B) = 0. No because P(A | B) ≠ P(A). No because P(A ∩ B) ≠ 0.

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Transcript

00:01 So we have a scenario in which we have a probability of something rising, of a stock rising, i believe is the way it is determined.

00:09 And that probability that a does is 0 .41.

00:13 The probability that b does is equal to .59.

00:19 And the probability of if b, which means conditional on b, that a does is equal to 0 .58.

00:25 And we want to find in part a, we want to find what is the probability that at least one does.

00:31 So either a or b or possibly both.

00:35 And so we know in order to find that we would add the probability of each event, but then we have to subtract away that intersection.

00:45 And we don't know that yet.

00:47 But we can find it from this because this probability is equivalent to the probability of a intersect.

00:55 B divided by the probability of b.

00:59 And we know that the probability of a intersect b is something we don't know.

01:06 But we know the probability of b is 0 .59.

01:09 And we know that this quotient is equal to that 0 .58.

01:15 So the probability of that intersection has to equal the product of 0 .59 times 0 .58.

01:24 So that's our intersection.

01:28 So to answer this question up here, we're going to take that 0 .41 plus the 0 .59 and subtract away that intersection.

01:39 So 0 .41 plus 0 .59 minus that intersection...

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