This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here's how to solve the problem using a tree diagram: a) Sketch a tree diagram to show all possible outcomes and their respective probabilities. Let P be the event that the feed is for pigs, and F be the event that the feed is for fowls. Let E be the event that the feed has expired, and E' be the event that the feed has not expired. Given probabilities: P(P) = 30% = 0.30 P(F) = 70% = 0.70 P(E | P) = 5% = 0.05 P(E' | P) = 1 - 0.05 = 0.95 P(E | F) = 10% = 0.10 P(E' | F) = 1 - 0.10 = 0.90 The tree diagram is structured as follows: ` Start ├─── Pig (P=0.30) ───┬─── Expired (P=0.05) ─── P(P and E) = 0.30 * 0.05 = 0.015 │ └─── Not Expired (P=0.95) ── P(P and E') = 0.30 * 0.95 = 0.285 │ └─── Fowl (P=0.70) ───┬─── Expired (P=0.10) ─── P(F and E) = 0.70 * 0.10 = 0.070 └─── Not Expired (P=0.90) ── P(F and E') = 0.70 * 0.90 = 0.630 ` b) Find the probability that the bag of feed has expired. To find the probability that a bag of feed has expired, we sum the probabilities of all paths leading to an expired bag. P(E) = P(P and E) + P(F and E) P(E) = (0.30 × 0.05) + (0.70 × 0.10) P(E) = 0.015 + 0.070 P(E) = 0.085 The probability that the bag of feed has expired is 0.085. That's 2 down. 3 left today — send the next one.