A stock market analyst figures the probabilities that two related stocks, A and B, will go up in price. She finds the probability that A will go up to be 0.6 and the probability that both stocks will go up to be 0.4 What should be her estimate of the probability that stock B goes up, given that stock A goes up?
0.2
56
To estimate the probability that stock B goes up, given that stock A goes up, we can make use of conditional probability. The conditional probability of an event B occurring, given that event A has already occurred, can be represented as P(B|A).
In this scenario, we know the probability of stock A going up is 0.6, denoted as P(A) = 0.6, and the probability of both stocks A and B going up is 0.4, denoted as P(A and B) = 0.4.
To find the probability that stock B goes up, given that stock A goes up, we use the formula for conditional probability:
P(B|A) = P(A and B) / P(A)
Substituting the given values into the formula:
P(B|A) = 0.4 / 0.6
Therefore, the estimate of the probability that stock B goes up, given that stock A goes up, is approximately 0.67 (or 67%).
To estimate the probability that stock B goes up, given that stock A goes up, we can make use of conditional probability.
In this case, we are given the probability that stock A goes up (P(A) = 0.6) and the probability that both stocks A and B go up (P(A and B) = 0.4).
The formula for conditional probability is:
P(B|A) = P(A and B) / P(A)
Substituting the given values, we have:
P(B|A) = 0.4 / 0.6
P(B|A) = 2/3
Therefore, the analyst should estimate the probability that stock B goes up, given that stock A goes up, to be 2/3 or approximately 0.67.