Eryn has just bought two stocks: A and B.She estimates that stock A has an 80% chance of increasing in value.She estimates that stock B has a 70% chance of increasing in value.She also estimates that if stock A increases in value, the chance that stock B will increase jumps to 75%.What's the probability that at least one of the stocks will increase in value?
A).24
B).20
C).26
D).90
E).56

Question

Quizplus · Accepted Answer

The probability that at least one stock increases in value is calculated by subtracting the probability that neither stock increases in value from 1. The probability that stock A does not increase is 20% (100% - 80%), and the probability that stock B does not increase given A does not increase is 30% (100% - 70%). However, since the probability of B increasing is dependent on A, we calculate the probability of both not increasing directly: P(A' and B') = P(A') * P(B'|A') + P(A') * P(B'). But since we're interested in at least one increasing, we use the complement. The direct calculation involves finding the probability of at least one increasing: P(A or B) = 1 - P(A')P(B'). Since we're not given P(B'|A'), we calculate directly: P(A or B) = 1 - (0.2 * 0.3) = 1 - 0.06 = 0.94 or 94%. However, the correct approach without needing P(B'|A') is to use the given probabilities and the conditional probability to find the overall probability. P(at least one increases) = P(A increases) + P(B increases) - P(A and B both increase). P(A and B both increase) = P(A increases) * P(B increases given A increases) = 0.8 * 0.75 = 0.6. Thus, P(at least one increases) = 0.8 + 0.7 - 0.6 = 0.9 or 90%.

Eryn Has Just Bought Two Stocks: a and B