i. Probability that either business A or business B or both succeed:

P(A or B) = P(A) +P(B)−P (A and B)

Substituting the values:

P(A or B )= 0.65+0.75 − 0.4875 = 1.40 − 0.4875 = 0.9125

Thus, the probability that either business A or business B or both succeed is 0.9125 or 91.25%.

ii) Probability that only one of the businesses succeeds:

This is the probability that either A succeeds and B fails, or B succeeds and A fails. The formula is:

P(only one succeeds)=P(A and not B)+P(B and not A)

Where:

P(A and not

B) = P (A) × (1−P(B)) = 0.6 5× (1−0.75) = 0.65 × 0.25 = 0.1625

P (B and not A) = P (B) × (1−P(A)) = 0.75 × (1−0.65) =0.75 × 0.35 = 0.2625

Adding these together: P(only one succeeds) = 0.1625 + 0.2625 = 0.425

Thus, the probability that only one of the businesses succeeds is 0.425 or 42.5%.

iii. Probability that none of the two businesses succeed:

This is the probability that both A and B fail:

P (none succeed) = (1−P(A)) ×(1−P(B)) = (1−0.65) × (1−0.75) = 0.35×0.25 = 0.0875

Thus, the probability that none of the two businesses succeed is 0.0875 or 8.75%.