Answer:
the probability that the stock was in the Information Technology sector given that it had a dividend yield of 2.00% or higher is approximately 0.0698 or 6.98%.
Explanation:
To find the probability that the stock was in the Information Technology (IT) sector given that it had a dividend yield of 2.00% or higher, we can use Bayes' theorem.
Let's define the following events:
A: Stock is in the IT sector.
B: Stock has a dividend yield of 2.00% or higher.
We are given the following probabilities:
P(A) = 0.1233 (Probability of stock being in the IT sector)
P(B|A) = 0.2842 (Probability of stock having a dividend yield of 2.00% or higher, given that it is in the IT sector)
P(B|not A) = 0.4464 (Probability of stock having a dividend yield of 2.00% or higher, given that it is not in the IT sector)
We want to find P(A|B), the probability of the stock being in the IT sector given that it has a dividend yield of 2.00% or higher.
According to Bayes' theorem:
P(A|B) = (P(B|A) * P(A)) / P(B)
To find P(B), we can use the law of total probability:
P(B) = P(B|A) * P(A) + P(B|not A) * P(not A)
P(not A) = 1 - P(A) = 1 - 0.1233 = 0.8767 (Probability of stock not being in the IT sector)
Let's calculate P(B):
P(B) = P(B|A) * P(A) + P(B|not A) * P(not A)
= 0.2842 * 0.1233 + 0.4464 * 0.8767
≈ 0.1076 + 0.3927
≈ 0.5003
Now, we can calculate P(A|B) using Bayes' theorem:
P(A|B) = (P(B|A) * P(A)) / P(B)
= (0.2842 * 0.1233) / 0.5003
≈ 0.0349 / 0.5003
≈ 0.0698
Therefore, the probability that the stock was in the Information Technology sector given that it had a dividend yield of 2.00% or higher is approximately 0.0698 or 6.98%.