Probability — Set #1 | Practice

{"setId":"2a6f8e71-b040-4296-a791-c001fc32ddbf","setTitle":"most-asked-questions","topicName":"Probability","topicSlug":"probability","setNumber":1,"totalQuestions":10,"questions":[{"id":"e24a0a1a-8abc-4bcc-9275-0c28d1ed726e","order":1,"statement":"A bag contains 5 red balls, 4 blue balls, and 3 green balls. If one ball is drawn at random, what is the probability that it is either red or green?","options":{"A":"2/3","B":"5/12","C":"1/2","D":"2/12"},"correctOption":"A","solution":"Total balls = 5+4+3 = 12. P(red) = 5/12, P(green) = 3/12. Since events are mutually exclusive, P(red or green) = 5/12 + 3/12 = 8/12 = 2/3."},{"id":"82f878e3-d08a-41f8-a28f-e2cff974c1ad","order":2,"statement":"Two dice are rolled together. What is the probability that the sum of the numbers on them is 8?","options":{"A":"5/36","B":"1/6","C":"7/36","D":"1/9"},"correctOption":"A","solution":"Total outcomes = 36. Pairs summing to 8: (2,6),(3,5),(4,4),(5,3),(6,2) = 5 outcomes. Probability = 5/36."},{"id":"31e9cfea-2a79-4256-9dbe-053f09bd7710","order":3,"statement":"A card is drawn at random from a well-shuffled deck of 52 cards. What is the probability that it is either a king or a heart?","options":{"A":"4/13","B":"17/52","C":"1/13","D":"15/52"},"correctOption":"A","solution":"P(king) = 4/52, P(heart) = 13/52, P(king and heart) = 1/52 (king of hearts, since it is both). Using P(A or B) = P(A)+P(B)-P(A and B) = 4/52+13/52-1/52 = 16/52 = 4/13."},{"id":"56dc8ec7-9a8b-4c71-86aa-f9524fbee37c","order":4,"statement":"In a class of 30 students, 18 study Mathematics, 12 study Physics, and 6 study both. If a student is selected at random, what is the probability that the student studies neither subject?","options":{"A":"1/5","B":"1/6","C":"3/10","D":"2/15"},"correctOption":"A","solution":"Students studying Math or Physics = 18+12-6 = 24. Students studying neither = 30-24 = 6. Probability = 6/30 = 1/5."},{"id":"80cc219c-6356-4bc6-b699-d047b93b3258","order":5,"statement":"A coin is tossed 3 times. What is the probability of getting at least 2 heads?","options":{"A":"3/8","B":"1/2","C":"5/8","D":"1/4"},"correctOption":"B","solution":"Total outcomes = 2^3 = 8. Outcomes with at least 2 heads: HHH, HHT, HTH, THH = 4 outcomes. Probability = 4/8 = 1/2."},{"id":"493c9022-ca13-4ad2-8600-3e7ad07c1591","order":6,"statement":"A box contains 3 defective and 7 non-defective bulbs. Two bulbs are drawn at random without replacement. What is the probability that both are non-defective?","options":{"A":"7/15","B":"21/45","C":"7/10","D":"1/3"},"correctOption":"A","solution":"Total ways to choose 2 from 10 = 45. Ways to choose 2 non-defective from 7 = 21. Probability = 21/45 = 7/15."},{"id":"6dde23d1-d870-467c-a5db-d0064ba1fff9","order":7,"statement":"A committee of 3 people is to be selected from a group of 4 men and 5 women. What is the probability that the committee consists of exactly 2 men and 1 woman?","options":{"A":"10/28","B":"30/84","C":"5/14","D":"15/42"},"correctOption":"C","solution":"Total ways to select 3 from 9 = 84. Ways to select 2 men from 4 and 1 woman from 5 = 6*5 = 30. Probability = 30/84 = 5/14."},{"id":"005ee50e-401d-4a01-bc93-d76ffe0a651f","order":8,"statement":"A number is selected at random from the first 50 natural numbers. What is the probability that it is a multiple of 3 or 5?","options":{"A":"23/50","B":"13/25","C":"1/2","D":"27/50"},"correctOption":"A","solution":"Multiples of 3 up to 50 = 16, multiples of 5 = 10, multiples of 15 (both) = 3. Multiples of 3 or 5 = 16+10-3 = 23. Probability = 23/50."},{"id":"1dd92a82-6f81-4ce0-ab9b-1b39bc57a3ad","order":9,"statement":"Three unbiased coins are tossed simultaneously. What is the probability of getting exactly two tails?","options":{"A":"3/8","B":"1/4","C":"1/2","D":"1/8"},"correctOption":"A","solution":"Total outcomes = 8. Exactly two tails: HTT, THT, TTH = 3 outcomes. Probability = 3/8."},{"id":"ef521d2b-6eba-4d1b-b9cc-5f64a48839a6","order":10,"statement":"A and B are two independent events such that P(A) = 0.4 and P(B) = 0.5. What is the probability that at least one of the events occurs?","options":{"A":"0.7","B":"0.9","C":"0.2","D":"0.5"},"correctOption":"A","solution":"P(A or B) = P(A) + P(B) - P(A)*P(B) = 0.4 + 0.5 - (0.4*0.5) = 0.9 - 0.2 = 0.7."}]}