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 at least one of the projects is successful?
To find the probability that at least one of the projects is successful, we can calculate the complementary probability that both projects fail and subtract it from 1.
The probability that project A fails is 1 - 0.4 = 0.6.
The probability that project B fails is 1 - 0.6 = 0.4.
Since the success of the two projects is independent, the probability that both projects fail is 0.6 * 0.4 = 0.24.
Therefore, the probability that at least one of the projects is successful is 1 - 0.24 = 0.76, or 76%.
To find the probability that at least one of the projects is successful, we need to consider the probability of the complement, i.e., the probability that both projects fail, and subtract it from 1.
The probability that both projects fail can be calculated by multiplying the probabilities of failure for each project:
P(failure A) = 1 - P(success A) = 1 - 0.4 = 0.6
P(failure B) = 1 - P(success B) = 1 - 0.6 = 0.4
Since the success of the two projects is independent, the probability that both projects fail is equal to the product of their individual failure probabilities:
P(both projects fail) = P(failure A) * P(failure B) = 0.6 * 0.4 = 0.24
Therefore, the probability of at least one project being successful is:
P(at least one project successful) = 1 - P(both projects fail) = 1 - 0.24 = 0.76
Thus, the probability that at least one of the projects is successful is 0.76 or 76%.
To find the probability that at least one of the projects is successful, you need to calculate the probability that both projects fail and subtract that from 1.
Let's break down the calculation step by step:
Step 1: Calculate the probability that both projects fail.
To find the probability that both projects fail, you multiply the probabilities of the projects failing together. Since the success of the two projects is independent, this can be calculated as follows:
Probability of both projects failing = Probability of project A failing * Probability of project B failing
Given that project A has a 40% probability of success, the probability of project A failing is 1 - 0.4 = 0.6.
Similarly, the probability of project B failing is 1 - 0.6 = 0.4.
Probability of both projects failing = 0.6 * 0.4 = 0.24
Step 2: Calculate the probability that at least one project is successful.
To find the probability that at least one project is successful, we subtract the probability of both projects failing from 1.
Probability of at least one project being successful = 1 - Probability of both projects failing
Probability of at least one project being successful = 1 - 0.24 = 0.76
Therefore, the probability that at least one of the projects is successful is 0.76 or 76%.