A college professor has been studying the relationship between the attendance habits of his students and the grades they earn in his courses. A breakdown of 200 of his students revealed the following:
Attended regularly --- 160
Attended sometimes --- 40
Passed --- 170 and Failed --- 30
140 Passed and 20 Failed
30 Passed and 10 failed
Assume that a student is chosen at random. What is the probability that the student passes the course, given that the student attended class sometimes?
The probability of both/all events occurring is found by multiplying the individual events.
40/200 * 30/40 = ?
To find the probability that a student passes the course given that they attended class sometimes, we need to use conditional probability.
Conditional probability is the probability of an event occurring given that another event has already occurred. In this case, the event is passing the course, and the condition is attending class sometimes.
The formula to calculate conditional probability is:
P(A|B) = (P(A ∩ B)) / P(B)
Where:
P(A|B) is the probability of event A occurring given that event B has already occurred.
P(A ∩ B) is the probability of both events A and B occurring.
P(B) is the probability of event B occurring.
Here's how we can calculate the probability:
1. Calculate P(A ∩ B), which is the probability of both attending class sometimes and passing the course. From the given information, we know that 30 students passed and attended class sometimes, so P(A ∩ B) = 30/200 = 0.15.
2. Calculate P(B), which is the probability of attending class sometimes. From the given information, we know that 40 students attended class sometimes, so P(B) = 40/200 = 0.2.
3. Plug in the values into the formula:
P(A|B) = (P(A ∩ B)) / P(B) = 0.15 / 0.2 = 0.75.
Therefore, the probability that a student passes the course given that they attended class sometimes is 0.75 or 75%.