Prove or disprove. Given n (n > 1) events A. A,. .A, E5, then n PIA]- PIA, N A,] < PIJ4;]< P[A,] i=1
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![4. Prove or disprove. Given n (n > 1) events A,. A. . A, E 5, then
PA]-PΑ, Ω 4] < PIUAi] <PA
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- Picture an experiment that observes the # of computers in use at a five-computer lab. Let A, B be the events defined as A = {3,4,5} and B={1,3}. Using set notation (i.e. using {}), the event (A union B)^C where superscript denotes the complement, would be equal to:1. Let A and B be two events such that ACB, then P(AB)= 1,2,3/Q1. (22 points)] This question consists of 11 paragraphs. In each part, circle the correct an a. P(A) d.0 b. P(A) c. P(B) 2. How many different four-digit numbers can be formed from the digits 1,2,3,4,5,6,7 such that the first digit 3 or 6 also you cannot repeat the digit. a. 240 b.48 c. 120 3. If A, B and C are mutually independent events and that P(A) = 0.3, P(B) = 0.2, P(C) = 0.4. The probability that at least one of the events occur is a. 0.336 c. 0.024 b.0.664 d. 0.976 e. None 4. A box contains 3 red balls and 5 black balls. Balls are drawn randomly one at a time with replacement from the box. The probability that the third red ball is the seventh ball drawn is. a. 0.169 b.0.282 c. 0.179 d. 0.121 e. None 5. A box contains 20 balls, 13 of them are red and the rest are blue. Three balls are drawn randomly without replacement. The probability of getting at least I blue ball is. a) 0.749 b) 0.251 c) 0.479 d) 0.521 a. 0.4 b.…pls help me do this the answer is 6.a) 0.1791 b) 13 days
- Find the probability that a man asked to form a two digit number out of 2, 3, 5, 7, 9 would form 79 when, (a) repetitions are not allowed (b) repetitions are allowed.Your team has uniform numbers 1 to 25. What is the probability that your number is less than 9? P(less than 9)Two numbers are randomly picked from the ranges [-1,2] and [1,3]. a) Write the sample space.b) What is the probability that the sum of these two numbers is less than 4 but greater than 2?c) What is the probability that the sum of these two numbers equals 4?d) The sum of these two numbers is less than 4, greater than 2 and x is greater than yWhat are the chances of it happening?
- just using the definition of probability and the theorem on page 17 of the notes, prove thatfor any events A and B,P (A) + P (B) − 1 ≤ P (A ∩ B) ≤ P (A ∪ B) ≤ P (A) + (B).(Please label them as “Inquality I”, “First In-equality”, “Inequality A”, etc.)Note: You may use Venn diagrams as guides, but a picture is nota complete proof. give proofs in complete sentences and mathematicalwork4) One number is randomly picked from 1 to 120. a) How many numbers are multiple of 3 or multiple of 5, or both? b) What is the probability to pick TWO numbers (no repeats), which are both "multiples of 3, but not multiples of 5?" Answer in (1 in ___)b) Events A and B are such that P(A) = 3/5, P(B) = 4/15. Find P(A U B) if i) A and B are mutually exclusive events. ii) A and B are independent events.
- 64. Let n be a positive integer. Suppose we choose a sequence i1, 12,. between 1 and n at random. ..., in of integers (a) What is the probability that the sequence contains exactly n 2 different integers? (b) What is the probability that the sequence contains exactly n - 3 different integers?11 do a part onlyaddition rule cats and dogs Among a group of 500 pet owners who visit the same pet store, it is found that 345 have a cat, while 375 have a dog. There are 290 of these who have both a dog and a cat. Suppose one individual is chosen at random from this group of 500 pet owners. a) Find the probability the individual owns either a dog or a cat b) Find the probability the individual owns neither a dog nor a cat c) Find the probability the individual owns a dog but not a cat..
