Q.A company is comparing two investment proposals for the coming year. Proposal A gives a profit of ₹80,000 with probability 0.4, ₹20,000 with probability 0.4, and a loss of ₹30,000 with probability 0.2. Proposal B gives a profit of ₹50,000 with probability 0.6, ₹10,000 with probability 0.3, and a loss of ₹5,000 with probability 0.1. Find the expected profit of each proposal, and state which proposal should be preferred on the basis of expected profit alone.

The expected profit of each proposal is found by weighting every possible outcome by its own probability and adding, then the two expected profits are compared directly. …

Proposal A — checking the distribution first: probabilities are $0.4+0.4+0.2=1$, so the distribution is valid.

Proposal B — checking the distribution first: probabilities are $0.6+0.3+0.1=1$, so the distribution is valid.

Cross-check for A, adding the terms in a different order: $(-6{,}000) + 32{,}000 = 26{,}000$; then $26{,}000+8{,}000=34{,}000$ — same total. Cross-check for B: $30{,}000 - 500 = 29{,}500$; then $29{,}500+3{,}000=32{,}500$ — same total. Both expected profits are confirmed.

Comparison: $E(A) = ₹34{,}000 > E(B) = ₹32{,}500$, so Proposal A gives the higher expected profit, by ₹1,500. …

A common mistake is forgetting to treat the loss figure as a negative value when multiplying by its probability (e.g. using $+30{,}000\times0.2$ instead of $-30{,}000\times0.2$), which would overstate th …