1. **State the problem:** Mr. Osei wants to invest a loan of 100000 in either the phone accessories business or the mobile money business. We need to determine which business has a higher probability of success when he fully supervises it, considering the given probabilities. 2. **Given data:** - Probability of full supervision, $P(S) = 0.62$ - Probability of no supervision, $P(\neg S) = 1 - 0.62 = 0.38$ - Success probability with full supervision: - Mobile money, $P(M|S) = 0.85$ - Phone accessories, $P(P|S) = 0.92$ - Success probability without supervision: - Mobile money, $P(M|\neg S) = 0.062$ - Phone accessories, $P(P|\neg S) = 0.048$ 3. **Calculate overall success probability for each business:** Using total probability theorem: $$ P(\text{success}) = P(S) \times P(\text{success}|S) + P(\neg S) \times P(\text{success}|\neg S) $$ - Mobile money: $$ P(M) = 0.62 \times 0.85 + 0.38 \times 0.062 = 0.527 + 0.02356 = 0.55056 $$ - Phone accessories: $$ P(P) = 0.62 \times 0.92 + 0.38 \times 0.048 = 0.5704 + 0.01824 = 0.58864 $$ 4. **Interpretation:** - Probability of success is higher for the phone accessories business ($0.58864$) than for the mobile money business ($0.55056$). 5. **Consider monthly profits:** - Phone accessories profit = 10000 - Mobile money profit = 3500 6. **Expected monthly profit considering success probabilities:** - Mobile money expected profit: $$ 0.55056 \times 3500 = 1926.96 $$ - Phone accessories expected profit: $$ 0.58864 \times 10000 = 5886.4 $$ 7. **Conclusion:** Since the phone accessories business has both a higher probability of success and a higher expected profit, Mr. Osei should invest the loan in the phone accessories business when full supervision is important.