Alec is taking a Statistics class and a Geography class. The probabilities that he passes these two classes are independent. The probability of him passing his Statistics class is 0.95. The probability of him passing his Geography class is 0.74.
What is the probability he fails one class, but passes the other?
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
P(pass Geog) = .05 * .74 = ?
P(pass Stat) = .95 * .26 = ?
Either-or probabilities are found by adding the individual probabilities.
To find the probability that Alec fails one class but passes the other, we can use the concept of complementary probability. First, let's find the probability that Alec passes both his classes:
Probability of passing Statistics class = 0.95
Probability of passing Geography class = 0.74
Since these two events are independent, we can multiply their probabilities:
P(passing both classes) = 0.95 * 0.74
Next, we need to find the probability that Alec fails one class. We have two cases:
1. Alec passes Statistics class and fails Geography class:
Probability of passing Statistics class = 0.95
Probability of failing Geography class = 1 - 0.74 = 0.26
P(passing Statistics and failing Geography) = 0.95 * 0.26
2. Alec fails Statistics class and passes Geography class:
Probability of failing Statistics class = 1 - 0.95 = 0.05
Probability of passing Geography class = 0.74
P(failing Statistics and passing Geography) = 0.05 * 0.74
Finally, we can calculate the probability that Alec fails one class but passes the other by adding the probabilities of these two cases:
P(fails one class, passes the other) = P(passing Statistics and failing Geography) + P(failing Statistics and passing Geography)
P(fails one class, passes the other) = (0.95 * 0.26) + (0.05 * 0.74)
Simplifying the equation:
P(fails one class, passes the other) = 0.247 + 0.037
P(fails one class, passes the other) = 0.284
Therefore, the probability that Alec fails one class but passes the other is 0.284 or 28.4%.