Question

1. A bag contains 10 black marbles, 8 red marbles, 7 yellow marbles. If one marble is drawn from the bag then replaced, what is the probability of drawing a black marble then a yellow marble?

2. In a number guess game you ask a person to guess a number from 1 to 10. If the person makes a random guess, what is the probability their guess will be less than 4?

3. A bag contains 8 blue marbles, 7 yellow marbles, 10 red marbles. If one marble is drawn from the bag but not replaced, what is the probability of drawing a blue marble then a red marble?

Answer 1

1. Since draw is with replacement, the Total number of marbles = 10 + 8 + 7 = 25 remains the same in each trial.

So,

P(Black in Draw 1) = 10/25 = 0.4

P(Yellow in Draw 2) = 7/25 = 0.28

So,

P(Black in Draw 1 & Yellow in Draw 2) = 0.4 X 0.28 = 0.112

2. Total number of Events = 10

Favorable Events = {1,2,3}

So,

P(less than 3) = 3/10 = 0.3

3.

Draw 1: Blue

Total Marbles = 25

Blue = 8

So,

P(Draw 1: Blue) = 8/25 = 0.32

After drawing 1 Blue:

Draw 2: Red

Total Marbles = 24

Red= 10

So,

P(Draw 2: Red = 10) = 10/24 = 0.4167

So,

P(Draw 1: Blue & Draw 2: Red) = 0.32 X 0.4167 = 0.1333