contestada

Two marbles are selected from a bag containing two red marbles, two blue marbles, and one yellow marble. The color of each marble is recorded.
Determine the sample space for the experiment.

Respuesta :

Answer:

(a) {RR,BB,RB,RY,BY}

(b) {R1 R2, R1 B1, R1 B2, R1 Y, R2 R1, R2 B1, R2 B2, R2 Y, B1 R1, B1 R2, B1 B2, B1 Y, B2 R1, B2 B1, B2 R2, B2 Y, Y R1, Y R2, Y B1, Y B2}.

Step-by-step explanation:

This question can be answered in two ways :

(a) When order of picking marbles does not matter.

(b) When order of picking marbles does matter.

  1. So, First I will explain what will be the sample space for the experiment when order of picking marbles does not matter.

Red marbles in the bag = 2

Blue marbles in the bag = 2

Yellow marbles in the bag = 1

Now since we have to select two marbles from the bag, the sample cases will be:

  • Both of the marbles could be Red.
  • Both of the marbles could be Blue.
  • One marble is Red and other one is Blue.
  • One marble is Red and other one is Yellow.
  • One marble is Blue and other one is Yellow.

In short Sample space = {RR,BB,RB,RY,BY} where R = Red , B = Blue and Y = Yellow.

    2. Now I will explain what will be the sample space for the experiment  when order of picking marbles does matter.

For this, First give numbers to the balls in bag i.e.,

First Red ball in the bag = R1

Second Red ball in the bag = R2

First Blue ball in the bag = B1

Second Blue ball in the bag = B2

Yellow ball in the bag = Y

Now the cases for sample spaces when two marbles are selected will be :

{R1 R2, R1 B1, R1 B2, R1 Y, R2 R1, R2 B1, R2 B2, R2 Y, B1 R1, B1 R2, B1 B2, B1 Y, B2 R1, B2 B1, B2 R2, B2 Y, Y R1, Y R2, Y B1, Y B2}.

Otras preguntas