EXERCISE A ball is drawn randomly from a bag containing 8 red, 4 blue and 2 green identical balls. Find the probability that the ball drawn is not red.

What is the probability that a number chosen at random from the integers between 1 and 10 inclusive is either a prime or a multiple of 3?

A bag contains four red balls, five blue balls and six green balls. Three balls are drawn from the bag at random without replacement. What is the probability that all three are:
The same colour
Different colour

1)The probability that the ball drawn is not red is 6 /14

2)Probability of getting either a prime or a multiple of 3 is 7/10

3)Probability of  drawing three balls without replacement such that all three are Same colour  is 0.0747

Probability of drawing three balls without replacement such that all three are different colour is 0.5

Step-by-step explanation:

1) A ball is drawn randomly from a bag containing 8 red, 4 blue and 2 green identical balls. Find the probability that the ball drawn is not red.

No. of red balls = 8

No. of blue balls = 4

No. of green balls = 2

Total no. of balls = 8+4+2=14

P(Getting red bal)=

P( ball drawn is not red) =

So,the probability that the ball drawn is not red is 6 /14

2)What is the probability that a number chosen at random from the integers between 1 and 10 inclusive is either a prime or a multiple of 3?

Numbers : 1 ,2,3,4,5,6,7,8,9,10

Prime numbers: 2,3,5,7 = 4

Multiple of 3 = 3,6,9 =3

So, Probability of getting prime number =

Probability of getting multiple of 3 =

So, Probability of getting either a prime or a multiple of 3=

Hence  Probability of getting either a prime or a multiple of 3 is 7/10

3)A bag contains four red balls, five blue balls and six green balls. Three balls are drawn from the bag at random without replacement. What is the probability that all three are:

The same colour

Different colour

No. of red balls = 4

No. of blue balls = 5

No. of green balls = 6

Total balls = 15

Case 1 :all three are Same colour

So, probability of  drawing three balls without replacement such that all three are Same colour =

So, probability of drawing three balls without replacement such that all three are different colour =

So,probability of  drawing three balls without replacement such that all three are Same colour  is 0.0747

So,probability of drawing three balls without replacement such that all three are different colour is 0.5

required rate of return = 0.166 = 16.6%

step-by-step explanation:

under the capital asset pricing model (capm), the required or expected rate of return for a particular security or asset is given using the formula:

required rate of return = risk-free rate + beta*(market risk premium)

we are given that;

risk-free rate = 4% = 0.04

beta = 1.4

market risk premium = 9% = 0.09

we simply plug these values into the above formula;

required rate of return = 0.04 + 1.4*(0.09)

required rate of return = 0.04 + 0.126

required rate of return = 0.166 = 16.6%