An oil exploration company currently has two projects. The company estimates that there is a 40% probability that project A is successful, a 60% probability that project B is successful, and that the success of the two projects is independent.
What is the probability that only project A succeeds and not project B?
To find the probability that only project A succeeds and not project B, we need to multiply the individual probabilities of each project.
The probability of project A succeeding is 40%.
The probability of project B not succeeding is 100% - 60% = 40%.
Since the success of the two projects is independent, we can multiply the probabilities:
P(A succeeds and B does not) = 0.40 * 0.40 = 0.16
Therefore, the probability that only project A succeeds and not project B is 0.16, or 16%.
To find the probability that only project A succeeds and not project B, we need to multiply the probability of project A succeeding by the probability of project B not succeeding.
Let's denote the probability of project A succeeding as P(A) and the probability of project B not succeeding as P(not B).
According to the information given:
P(A) = 0.40 (40% probability that project A is successful)
P(not B) = 1 - P(B) = 1 - 0.60 = 0.40 (60% probability that project B is not successful)
To find the probability of both events occurring, we multiply these probabilities:
P(A and not B) = P(A) x P(not B)
= 0.40 x 0.40
= 0.16
Therefore, the probability that only project A succeeds and not project B is 0.16 (16%).
To find the probability that only project A succeeds and not project B, we need to multiply the probability of project A being successful, by the probability of project B failing.
Given that the success of the two projects is independent, we can use the multiplication rule of probability.
The probability of project A's success is given as 40% or 0.4.
The probability of project B's failure is 1 minus the probability of success, so it would be 100% minus 60%, which is 40% or 0.4.
Using the multiplication rule, the probability that only project A succeeds and not project B is:
Probability(A succeeds and B fails) = Probability(A succeeds) * Probability(B fails)
= 0.4 * 0.4
= 0.16 or 16%.
Therefore, the probability that only project A succeeds and not project B is 16%.