Tiêu đề WK1 - Y5 - MATH - HW - PROBABILITY - AN.docx.pdf ✅

Question 1: Step 1: In a box containing a dozen pens, 3 are defective. Big Bird randomly selects one pen from the box. There are a total of 12 pens. 3 are defective, the non-defective pens are 12 - 3 = 9 pens. Step 2: The probability of selecting a non-defective pen is - 9/12 The probability of selecting a second non-defective pen is - 8/11 Then, the probability is - 9/12 * 8/`11 = 6/11 Answer: E. 6/11 Question 2: Step 1: The probability that it will rain tomorrow is 35 percent. Step 2: Then, the probability that it will not rain tomorrow is - 100% - 35% = 65%. Answer: C. 65 percent Question 3: Step 1: Two dice are rolled. There are 21 outcomes where the sum is greater than 6. There are a total of 11 outcomes where at least one dice shows 6. {(1,6), (2,6), (3,6), (4,6), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)} Step 2: Then, the probability is - P(At least one 6 | Sum greater than 6) = 11/21. Answer: D. 11/21 Question 4: Step 1: A box only contains red tokens and blue tokens. The probability of randomly selecting a red token from the box is 3/7. ©Scholarly 2025. All rights reserved. All digital content and materials provided are proprietary and protected under copyright law. Any reproduction or sharing of digital files, including screenshots, recordings, or downloads, is strictly prohibited without the prior written consent of Scholarly. 1
There are 40 blue tokens in the box. Say there are x red tokens in the box. Step 2: x/(40 + x) = 3/7 7x = 120 + 3x 4x = 120 x = 120/4 = 30 So, there are 30 red tokens in the box. Answer: A. 30 red tokens Question 5: Step 1: A number is randomly chosen from the first 200 positive numbers. The total numbers that are multiple of 3 between 1 to 200 is - 200/3 = 66.66 or 66. The total numbers that are multiple of 5 between 1 to 200 is - 200/5 = 40. Step 2: The numbers that are multiple of both 3 and 5 are also a multiple of 15. The numbers that are multiple of 15 is - 200/15 = 13.333 or 13. The total number of integers that are multiples of 3 or 5 is - 66 + 40 - 13 = 93. The number of integers that are either multiples of 3 or multiples of 5, but not both, is - 93 - 13 = 80. The probability is - 80/200 = 0.4 or 2/5. Answer: B. 2/5 Question 6: Step 1: Total Number of Cards: There are 12 + 18 + 5 = 35 cards in total. Favorable Outcomes: The favorable outcomes are the cards that are either marked with a star or a circle. There are 12 star cards and 5 circle cards, so the total number of favorable outcomes is 12 + 5 = 17. Step 2: Probability: The probability is the ratio of favorable outcomes to total outcomes, which is 17/35. ©Scholarly 2025. All rights reserved. All digital content and materials provided are proprietary and protected under copyright law. Any reproduction or sharing of digital files, including screenshots, recordings, or downloads, is strictly prohibited without the prior written consent of Scholarly. 2