Question

Calculate the probability that the number 89 will come out when taking a ball from a bag with 120 balls numbered from 1 to 120.

Calculate the probability that "a number between 1 and 125" will come out when removing a ball from a bag with 130 balls numbered from 1 to 130.

If four questions with four options each are answered randomly, what is the probability of matching all of them?

Calculate the probability that "a number between 1 and 3" will come out when rolling a die.

If a die is rolled and the result is observed: What is the probability that a 6 does not come out?

Answer 1

Q1. There are 120 balls , each have different number from 1 to 120

There is one ball numbered 89

Probabilty of an event = favorable number of case / total number of cases

Here total number of cases = 120

favorable number of cases = 1

Probability that the number 89 will come out = 1/ 120 = 0.0083

Q2. Total number of cases = 130

favorable number of cases = 125 ( there are 125 balls numbered between 1 to 125)

Probability that a ball numbered between 1 to 125 will come out = 125 / 130 = 0.9615

Q3. There are 4 options to each question ( one correct , three wrong)

If the answer is selected randomly , probability answering correctly a single question = 1/4 = 0.25

As each question is answered independently and probability of correct answer is same for all, we use Binomial distribution

Let X be the number of questions answered correctly

X follow Binomial with n = 4 , p =0.25

Probability mass function of X is

Probability of matching all the questions = 0.0039

Q4. In a die there are 6 faces numbered 1,2,3,4,5and 6

When rolling a die , total number of cases = 6

Favorable number of cases of rolling between 1 and 3 = 3

Probability of rolling between 1 and 3 = 3/6 =0.5

Q5.  

In a die there are 6 faces numbered 1,2,3,4,5and 6

When rolling a die , total number of cases = 6

Favorable number of cases of rolling number 6  = 1

Probability that 6 come out = 1/6

Probability that 6 does not ccome out = 1-1/6 = 5/6 = 0.8333