Question

Ps A random experiment can result in one of the outcomes (a b, dh with respective probabilities of o2, 02, 05.0.1. Let A denote the event (a. b). B the event (b, c, d and C the event (d). 1) Find P(A U C. 2) P(A intersection B) Each sample of water has a 5% chance of containing a particular organic pollutant Assume that the samples are independent with regard to the presence of the pollutant. Find the probability that in the next 25 samples, exactly 3 contain the pollutant solve this problen the formula for a binomiai datribution T he probability that a bit transmitted through a digital transmission channel is received in error is 0.16. Assume the transmissions are independent events, and let the random variable X denote the number af bits transmitted until the first error. Find Px 4, using the fomula for a geometric random varlable and pix-3) nswerl A batch of parts contains 100 parts from a local supplier of tubing and 210 parts froma supplier of tubing in the next state. 6 parts are selected randomly and without replacement and let the random varialble X represent the number of parts in the sample from the local supplier Find Epx) Hunt Use the formula far the expected value of a Hypergeometric rondom vanable) Onestios 8 Consider a test for two sided 95% C, calculate Z and the management gave variability info as 2 Find the number of specimens ln) that must be tested to ensure that the 95% Confidence Interval has a length of at most 1.3. Ans

Answer 1

4)

From given information we have

P(a) = P(b) = 0.2, P(c) = 0.5, P(d) =0.1

1)

$A\cup C = (a,b,d)$

So,

$P(A\cup C) =P(a)+P(b)+P(d)=0.2+0.2+0.1=0.5$

2)

$A\cap B= (b)$

So,

$P(A\cap B)= P(b)=0.20$