Statistics and Probability Answers

The probability of conducting an examination on time is 0.95 if there is no strike by students and 0.25 if there is a strike. If the probability that there will be a strike is 0.65, find the probability of holding the examination on time.

Bag A contains 2 White and 4 Black balls. Another bag B contains 5 white and 7 black balls. A ball is transformed from the bag A to the bag B. Then a ball is drawn from the bag B. Find the probability that it is Black.

If A and B are two events with probabilities 0.25 and 0.5 corresponding to A and A∪B respectively, then find the probability of B if (i) A and B are mutually exclusive (ii) A and B are independent (iii) B contains A.

The sales per day in a shop is exponentially distributed with average sale amounting to Rs.100 and net profit is 8%. Find the probability that the net profit exceeds Rs.30 on two consecutive days.

The height of adult women in the United States is normally distributed with mean 64.5 inches and standard deviation 2.4 inches. Find the probability that a randomly chosen woman is
(a) Less than 63 inches tall
(b) Less than 70 inches tall
(c) Between 63 and 70 inches tall
(d) Alice is 72 inches tall. What percentage of women are shorter than Alice?
(e) Find the probability that the average of the heights of two randomly chosen women is greater than 67.5 inche

Suppose that the percentage annual return you obtain when you invest a dollar in gold or the stock market is dependent on the general state of the national economy as indicated below. For example, the probability that the economy will be in "boom" state is 0.15. In this case, if you invest in the stock market your return is assumed to be 25%; on the other hand if you invest in gold when the economy is in a "boom" state your return will be minus 30%. Likewise for the other possible states of the economy. Note that the sum of the probabilities has to be 1--and is.

State of economy Probability Market Return Gold Return
Boom 0.15 25% (-30%)
Moderate Growth 0.35 20% (-9%)
Week Growth 0.25 5% 35%
No Growth 0.25 (-14%) 50%

Based on the expected return, would you rather invest your money in the stock market or in gold? Why?

a fair coin is tossed until for the first time the same result appears twice in succession(i.e until the TT or HH).Describe the sample space and assign probabilities that reflects the fairness of the coin..find the probabilities of the events
A="The coin is tossed at most five time"
B="the total number of tossed is odd'"
C=AUB
D= A(intersection)B

A planning committee for a major development project must consist of four architects, three engineers and one environmental lawyer. There are six architects, five engineers and 3 environmental lawyers available to choose from. How many different combinations of the committee can be formed (rounded off to zero decimals)?

Twenty prominent citizens have been nominated for a 'Community Citizen of the Year' award. First- and second-place trophies are awarded to the two persons receiving the highest and second highest number of votes. In how many different ways can the first and second place trophies be awarded (rounded off to zero decimals)?

Let x be a continuous random variable with the probability distribution defined by
p(x)= {kx^2, 0<=x<=3
={0,else where

Evaluate k and find (i) P(1 ≤ x < 2), (ii) P(x ≤ 1),
(iii) P(x > 1). Also find the mean and variance of the distribution.

Let X, and Y be two independent random variables such that E(X)=2, Var(X)=4, E(Y)=7, and Var(Y)=1. Find: 1). E(3X+7) and Var(3X+7) 2). E(5X+2Y-2) and Var(5X+2Y-2).
(b) If two random variables have the joint density
Find the probability that