Let A and B be events such that P(B)=0.28, P(B|A) =0.44 and P(A or B)=0.63, What is P(A)
To find the probability of event A, you need to use the formula for conditional probability and the principle of inclusion-exclusion.
First, let's break down the given information:
1. P(B) = 0.28: This means the probability of event B occurring is 0.28.
2. P(B|A) = 0.44: This means the probability of event B occurring given that event A has already occurred is 0.44.
3. P(A or B) = 0.63: This means the probability of either event A or event B occurring (or both) is 0.63.
Now, let's proceed step by step to find P(A):
Step 1: Use the principle of inclusion-exclusion
P(A or B) = P(A) + P(B) - P(A and B)
Step 2: Substitute the given values
0.63 = P(A) + 0.28 - P(A and B)
Step 3: Rearrange the equation
P(A) = 0.63 - 0.28 + P(A and B)
Step 4: Use the definition of conditional probability
P(A and B) = P(B|A) * P(A)
Step 5: Substitute the given values
P(A) = 0.63 - 0.28 + (0.44 * P(A))
Step 6: Simplify the equation
P(A) = 0.35 + 0.44 * P(A)
Step 7: Move the term involving P(A) to one side of the equation
P(A) - 0.44 * P(A) = 0.35
Step 8: Simplify the equation further
0.56 * P(A) = 0.35
Step 9: Solve for P(A)
P(A) = 0.35 / 0.56
Step 10: Calculate the value of P(A)
P(A) ≈ 0.625
Therefore, the probability of event A (P(A)) is approximately 0.625.