the probability that she gets a basket the fire. the probability that she gets a basket the second is 0.4 . a ara could get a basket either time. Show the is 0.9 . the different possible outcomes in. What is the most likely outcome? a Find the probability that Zara gets at least one basket. amary checklist

We are told that Zara takes two shots. The probability she makes the second shot is given as 0.4. It is also stated that the probability she gets a basket on either shot (i.e. at least one basket) is 0.9. We are to: 1. Find the probability that she makes the basket on her first shot. 2. List the different possible outcomes (with their probabilities). 3. Identify the most likely outcome. 4. Confirm that the probability of making at least one basket is indeed 0.9. Step 1. Find the probability of a basket on the first shot. Let p be the probability that Zara makes the basket on her first shot. We assume the two shots are independent. Then the probability that she misses the first shot is (1 – p) and that she misses the second shot is (1 – 0.4) = 0.6. So the probability that she misses both shots is   (1 – p) × 0.6. We are told the probability that she makes at least one basket is 0.9. Since “at least one basket” is the complement of “no baskets,”   P(at least one) = 1 – [Probability of missing both]. Thus, we have   1 – [(1 – p) × 0.6] = 0.9. Solving for p:   (1 – p) × 0.6 = 1 – 0.9 = 0.1   1 – p = 0.1 / 0.6 ≈ 0.1667   p = 1 – 0.1667 ≈ 0.8333. So the probability of making the first basket is about 5/6 (approximately 0.8333). Step 2. List the possible outcomes and their probabilities. There are four possible outcomes for two shots. We’ll denote “B” for a made basket and “M” for a miss. a) Outcome MM (miss both):   Probability = (1 – p) × 0.6 ≈ 0.1667 × 0.6 = 0.1 b) Outcome BM (basket on first, miss on second):   Probability = p × 0.6 ≈ 0.8333 × 0.6 = 0.5 c) Outcome MB (miss on first, basket on second):   Probability = (1 – p) × 0.4 ≈ 0.1667 × 0.4 ≈ 0.0667 d) Outcome BB (basket on both shots):   Probability = p × 0.4 ≈ 0.8333 × 0.4 ≈ 0.3333 You can check that these add to 1:   0.1 + 0.5 + 0.0667 + 0.3333 = 1.0 Step 3. What is the most likely outcome? From the outcomes above:   MM: 0.1   BM: 0.5   MB: 0.0667   BB: 0.3333 Thus, the most likely outcome is “Basket on the first shot and Miss on the second” (BM) with probability 0.5. Step 4. Confirm the probability of at least one basket is 0.9. The probability of at least one basket is the sum of the probabilities of outcomes BM, MB, and BB:   P(at least one) = 0.5 + 0.0667 + 0.3333 = 0.9. That matches the given information. Summary of Answers: 1. The probability that Zara makes the basket on her first shot is approximately 0.8333 (or 5/6). 2. The outcomes with probabilities are:   – MM (miss both): 0.1   – BM (basket first only): 0.5   – MB (basket second only): ≈0.0667   – BB (baskets on both): ≈0.3333 3. The most likely outcome is BM, i.e. making the first shot (basket) and missing the second shot, with probability 0.5. 4. The probability that Zara gets at least one basket is 0.9. This completes the solution.