A box contains 12 white and 8 black marbles. Two balls are drawn out randomly from...
A box contains 3 red and 4 green marbles. Five marbles are drawn without replacement. Let X denote the number of red marbles obtained. a) Construct the probability distribution of X. b) What is the expected number of red marbles?
5. Three boxes are numbered 1, 2 and 3. For k 1, 2, 3, box k contains k blue marbles and 5 - k red marbles. In a two-step experiment, a box is selected and 2 marbles are drawn from it without replacement. If the probability of selecting box k is proportional to k, then the probability that two marbles drawn have different colours is 6. Two balls are.dropped in such a way that each ball is equally likely to...
2. An urn contains six white balls and four black balls. Two balls are randomly selected from the urn. Let X represent the number of black balls selected. (a) Identify the probability distribution of X. State the values of the parameters corresponding to this distribution (b) Compute P(X = 0), P(X= 1), and P(X= 2). (c) Consider a game of chance where you randomly select two balls from the urn. You then win $2 for every black ball selected and...
(5) A box contains 4 red and 6 white balls. If two balls are drawn at random without replacement, find the probability that one of the two is red (6) A box contains 4 red and 6 white balls. If two balls are drawn at random with replacement, find the probability that one of the two is red
Box 1 contains a red balls and b white balls. Box 2 contains c red balls and d white balls. One ball is randomly drawn from Box 1 and put into Box 2, and then one ball is randomly drawn from Box 2 and put back in Box 1. Finally, one ball is drawn at random again from Box 2. Let X denote the number of red balls drawn from Box 2 the 2nd time. Write down the distribution of...
Suppose that a box contains 40 red balls, 30 black balls, and 20 yellow balls. A sample of five balls is drawn without replacement. Let x number of red, y number of black and z number of yellow Find the probability that x 1, y 1, and z=3. Find the joint pdf of X and Z а. b
Two marbles are drawn randomly one after the other without replacement from a jar that contains 4 red marbles, 2 white marbles, and 7 yellow marbles. Find the probability of the following events. (a) A red marble is drawn first followed by a white marble. The probability is : (b) A white marble is drawn first followed by a white marble. The probability is : (c) A yellow marble is not drawn at all. The probability is :
1. We draw randomly without replacement 3 balls from an urn that contains 3 red and 5 white balls. Denote by X the number of red balls drawn. Find the probability distribution of X, its expected value, and its standard deviation.
2. A box contains 5 red balls, 7 white balls, and 8 black balls. Four balls are randomly chosen (without replace- ment). What is the probability that (a) 1 red ball, 2 white balls, and 1 black ball are chosen? (b) exactly two red balls are chosen? (c) the first chosen is black, the last three chosen are two white balls and one black ball?
7. Two marbles are drawn without replacement from a jar with 4 black and 3 white marbles Find the probability that: a. both are black b. the first is black and the second is white.