Final answer:
To find the probability of event A, use the multiplication rule for conditional probabilities. P(A) is found by dividing P(A AND B) by P(B|A), giving P(A) = 0.07 / 0.20, which equals 0.35.
Step-by-step explanation:
The question asks to calculate the probability of event A, given that P(B AND A) = 0.07 and P(B|A) = 0.20. The multiplication rule for conditional probabilities states that P(A AND B) = P(B|A)P(A). By rearranging this equation, we can solve for P(A) by dividing both sides by P(B|A), which gives us P(A) = P(A AND B) / P(B|A). Substituting in the values from the question, we get P(A) = 0.07 / 0.20 = 0.35. Therefore, the probability of event A occurring is 0.35.