The probability of all/both events occurring is found by multiplying the probabilities of the individual events.
.8 * x = .5
.8 * x = .5
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).
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%.