16:21. In order to test whether a coin is perfect, it is tossed 5 times. The null hypothesis ofperfectness of the coin is accepted if and only if atmost 3 heads are obtained. Then the power of the testcorresponding to the alternative hypothesis that probability of head is 0:4, is56(iii) 31252853272(1) 3125LE (ii)(iv) none of these.3125

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Answered: 16-21. In order to test whether a coin…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Q. 4 Let A, B, and C, be independent events with probabilities pa» Pp, Pc of occurring, respectively. (i) What is the probability all 3 events occurring? (ii) What is the probability of none of them occurring? (iii) What is the probability that exactly 1 occurs?
12 When two dice are thrown determine the probabilities from axiom 3 for the following three events. (i) A = { Sum = 7} (üi) C- {10 < Sum} and deiermine (ii) B (8 < Sum < 11} (iv) P (Bn C)
3. When a coin is tossed the probability that it will show heads is p. (The coin could be biased. So p need not be 1/2). If it is tossed repeatedly, assuming that the outcomes of the tosses are independent, what is the probability that there will be n – 1 tails in succession and the n-th toss will result in heads. ((1 – p)"-'p.) 4. In an experiment one tosses the coin of Problem 3 repeatedly until the first head shows. Then the experiment stops. What is the sample space? Verify that the sum of the probabilities of the outcomes is to 1. ( ΗΤΗ, ΤTH, . . .)
When coin 1 is flipped, it lands on heads with probability ; when coin 2 is flipped it lands on heads with probability. (a) If coin 1 is flipped 9 times, find the probability that it lands on heads at least 7 times. (b) If one of the coins is randomly selected and flipped 11 times, what is the probability that it lands on heads exactly 8 times? (c) In part (b), given that the first of these 11 flips lands on tails, find the conditional probability that exactly 8 of the 11 flips land on heads.
2" players of equal strength are playing a knock out tournament. If they are paired at randomly in all rounds, find out the probability that out of two particular players S₁ and S₂, exactly one will reach in semi-final (n = N, n ≥ 2).
Please solve very soon completely all parts
4
(2) A box contains 4 red balls, 3 green balls and 4 black balls. Three balls are drawn at random without replacement, and then the probability that the balls have same color is (а) 1/36 (b) 17/33 (c) 15/36 (d) 5/36 (e) 15/33 (f) None of these
One hundred cards are marked 00,01,02,03,...,09,10,11,.. .,99 One of the cards is selected at random. Find the probability that: (i) the digit 9 appears. (ii) the digit 9 does not appear. (iii) the card bears a double digit. (iv) the number on the card is a multiple of 9 (not 00). (v) the number on the card is a double digit or a multiple of 9. 6.
In a shipment of 100 parts, 4 are defective. The purchaser has time to test only 10 randomly selected parts for defects. Let X be the number of defective parts the purchaser finds.(a) Give the support X of X.(b) What is the probability that the purchaser finds no defective parts?(c) What is the probability that the purchaser finds at least 1 defective part?(d) Suppose the shipment has d defective parts. What is the largest value of d such that the probability is at least 0.90 that the purchaser finds no defects among 10 randomly sampled parts?
(3) A box contains 6 red balls, 7 green balls and 5 black balls. Three balls are drawn at random without replacement, and then the probability that the balls have same color is (а) 34/136 (b) 17/133 (c) 15/136 (d) 10/136 (e) None of these

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