here P(third bead is first white) =P(1st bead is black and 2nd black and 3rd white)
=(5*4*6)/(11*10*9)=4/33 =a/b
from above a =4 and b=33
therefore value of a+b =4+33 =37
3. There are 6 white beads and 5 black beads in your pocket. You randomly pull...
7. A jar contains 6 white beads and 3 black beads. Beads are chosen randomly from the jar one at a time until the third time a black bead turns up. a. Suppose that each bead is replaced before the next is chosen. How many beads should you expect to be chosen in the course of the experiment? [5] b. Suppose that if a bead is white, it is not replaced before the next bead is chosen, but if it...
A jar contains 6 white beads and 3 black beads. Beads are chosen randomly from the jar one at a time until the third time a black bead turns up. a. Suppose that each bead is replaced before the next is chosen. How many beads should you expect to be chosen in the course of the experiment? [5] b. Suppose that if a bead is white, it is not replaced before the next bead is chosen, but if it is...
7. A jar contains 6 white beads and 3 black beads. Beads are chosen randomly from the jar one at a time until the third time a black bead turns up. a. Suppose that each bead is replaced before the next is chosen. How many beads should you expect to be chosen in the course of the experiment? [5] b. Suppose that if a bead is white, it is not replaced before the next bead is chosen, but if it...
7. A jar contains 6 white beads and 3 black beads. Beads are chosen randomly from the jar one at a time until the third time a black bead turns up. a. Suppose that each bead is replaced before the next is chosen. How many beads should you expect to be chosen in the course of the experiment? [5] b. Suppose that if a bead is white, it is not replaced before the next bead is chosen, but if it...
Typed answers are preferrable over handwritten :) A jar contains 6 white beads and 3 black beads. Beads are chosen randomly from the jar one at a time until the third time a black bead turns up. a. Suppose that each bead is replaced before the next is chosen. How many beads should you expect to be chosen in the course of the experiment? [5] b. Suppose that if a bead is white, it is not replaced before the next...
An urn contains 10 white and 6 black balls. Balls are randomly selected, one at a time, until a black one is obtained. If we assume that each ball selected is replaced before the next one is drawn, what is the probability that a) exactly 5 draws are needed? b) at least 3 draws are needed?
A box contains 12 white and 8 black marbles. Two balls are drawn out randomly from the box without replacement. Let X denote the number of white balls drawn out. a. Construct the probability distribution of X. b. Find mean and variance of X using the following formula ? = E (X) = ∑ ? . ?(?) ? ?(?2) = ∑ ?2 . ?(?) ? ?2 = ???(?) = ?(?2) − (?)2
3. There are 6 balls in a bag with 2 being white and 4 black. If one draws 18 balls from the bag with replacement, let y be the number of black balls drawn. • Identify the name of the probability distribution of Y. Find its expected value and variance • Use Tchebysheff's inequality to estimate an upper bound of the probability that Y 38 or Y 2 16.
3. I have a box with 4 blue chips and 6 white chips. I randomly pull a chip from box 1and put it in box 2 which contains 3 blue chips and 8 white chips. Then I randomly pull a chip from box 2 and put it in box 3 which contains 6 blue chips and 3 white chips. a) What is the probability I pull a blue chip from box 3? b) What is the probability I pull a...
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...