Question

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 is black, it is replaced before the next is chosen. How many beads should you expect to be chosen in the course of the experiment? [10]

Answer 1

Answer:

A container contains 6 white globules and 3 dark dots. Dabs are picked arbitrarily from the container each in turn until the third time a dark globule turns up.

Let W speaks to the white globule ,B speak to the Block dot

Globule are picked arbitrarily until the third time a dark dots turns up

a)

On this each globule it supplanted before the following case it picked

So,number of ways we can choose 3 globule utilizing the above condition is

BBB + BWB + WBB + WWB

Here the quantity of methods of picking a dark globule is 3 and number of methods of picking a white dot is 6

So the necessary number of ways is

= 3*3*3 + 3*6*3 + 6*3*3 + 6*6*3

= 243

So the quantity of dabs should we hope to be picked in this course of the analysis is 243

b)

On the off chance that a white dab whenever picked than it isn't supplanted before the following globule is picked however on the off chance that it is black,it is supplanted before the following is picked

So the quantity of methods of picking dabs for this situation is

= BBB + BWB + WBB + WWB

= 3*3*3 + 3*6*3 + 6*3*3 + 6*5*3

= 225

So the quantity of dabs should we hope to be picked in this course of the analysis is 225