Final answer:
The probability of both independent events A and B occurring, represented as P(A AND B), is found by multiplying their probabilities: P(A AND B) = 0.1 × 0.7, resulting in P(A AND B) = 0.07 or 7%.
Step-by-step explanation:
When dealing with independent events, the probability of both events A and B occurring, denoted as P(A AND B), is calculated by multiplying their individual probabilities. Since we are given that events A and B are independent, and their respective probabilities are P(A)=0.1 and P(B)=0.7, the calculation step to find P(A AND B) is simple multiplication.
The formula to determine the probability of the conjunction of two independent events is:
P(A AND B) = P(A) × P(B)
By inserting the given probabilities into this product rule:
P(A AND B) = 0.1 × 0.7
This yields:
P(A AND B) = 0.07
Therefore, the probability that both events A and B occur together is 0.07, or 7%.