On tuesday you all took the science and then your social studies final exams. What is the probability of you passing your social studies final exam given that you know that you passed your science final exam first ? The probability of you passing both is 50% and the probability of you passing the first 80%
The probability of all/both events occurring is found by multiplying the probabilities of the individual events.
.8 * x = .5
To calculate the probability of passing the social studies final exam given that you passed the science final exam first, we need to apply conditional probability.
Step 1: Convert the given information into probabilities:
- Probability of passing both exams: P(A and B) = 50%
- Probability of passing the first exam (science): P(A) = 80%
Step 2: Use the conditional probability formula:
P(B|A) = P(A and B) / P(A)
Step 3: Substitute the given probabilities into the formula:
P(B|A) = 0.50 / 0.80
Step 4: Simplify the fraction:
P(B|A) = 0.625
Therefore, the probability of passing the social studies final exam given that you passed the science final exam first is 62.5% (or 0.625).
To find the probability of passing your social studies final exam given that you already passed your science final exam, we can use conditional probability.
Conditional probability is calculated using the formula: P(A|B) = P(A and B) / P(B), where P(A|B) represents the probability of event A occurring given that event B has already occurred.
In this case, event A is passing your social studies final exam, and event B is passing your science final exam.
Given information:
P(A and B) = 50% (probability of passing both exams)
P(B) = 80% (probability of passing the science final exam)
Now, let's substitute the values into the formula:
P(A|B) = (P(A and B)) / P(B)
P(A|B) = (50%) / (80%)
To find the probability, we can divide 50% by 80%:
P(A|B) = 0.5 / 0.8
Simplifying the division, we get:
P(A|B) = 0.625
Therefore, the probability of passing your social studies final exam given that you already passed your science final exam is 0.625, or 62.5%.