Maths · Probability: Probability of an event, addition and multiplication theorems of probability
Three numbers are chosen at random withoutreplacement from the set of integers T
Three numbers are chosen at random withoutreplacement from the set of integers \( 1,2,3, \ldots .10 . \) The probability that the minimum of thechosen numbers is 3 or the maximum of thechosen numbers is \( 7, \) is equal to
- A. \( 23 / 120 \)
- B. \( 13 / 120 \)
- C. \( 13 / 60 \)
- D. \( 11 / 40 \)
Step-by-step solution
Total ways to choose 3 numbers from 1-10: C(10,3)=120. Let A be event min=3: choose 3 and 2 from {4,...,10}: C(7,2)=21. P(A)=21/120. Let B be event max=7: choose 7 and 2 from {1,...,6}: C(6,2)=15. P(B)=15/120. Intersection A∩B: choose 3 and 7 and one from {4,5,6}: 3 ways. P(A∩B)=3/120. By inclusion-exclusion, P(A∪B)=21/120+15/120-3/120=33/120=11/40.
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