Question

Solve all the following questions from chapter 4 :
1) If a dice is thrown up one time, what is the probability of getting a number greater
than 2 or less than 5 ?
2) If two dice are thrown up once, what is the probability to get total numbers less
than 8 or at most 5 ?
3) If a dice is thrown up one time, what is the probability of getting an odd number
giving that the number is divided by 3 ?
4) If two dice are thrown up once, what is the probability to get total numbers greater
than 11 if the second number is 5 ?
5) If A , B are two events , P(A) = 0.5 , P(B) = 0.2 , P(A and B) = 0.4 , find P(A or B)
6) If A , B are two independent events , P(A) = 0.24 , P(B) = 0.31 , Find P(A or B)
7) If A , B are two events , P(B) = 0.8 , P(A and B) = 0.5 , find P(A \ B)
8) If A , B are two events , P(B) = 0.35 , P(A \ B) = 0.14 , find P(A and B)

Answer 1

Dear student, We can solve only 4 parts for a question, please help to upload others separately, I hope you understand. Please comment in the case of any doubt and I would love to clarify it.

P(A) = n(E)/n(S)

Where P(A) is the probability of an event A

n(E) is the number of favorable outcomes

n(S) is the total number of events in the sample space.

1)

If a die is rolled one time, the possible outcomes are 1,2,3,4,5,6. Total of 6 outcomes. The favorable outcomes should be greater than 2 or less than 5, it can be 3 and 4 then.

Probability of the number coming as 3 and 4 = 2/6 = 1/3

2)

Here, it should be at least 5 and not almost 5 as almost 8 is already given(total less than 8)

Hence, the total can be 5, 6 and 7

Cases for total 5 - (4,1) (1,4) (3,2) (2,3) ---- 4 cases

Cases for total 6 - (1,5) (5,1) (4,2) (2,4) (3,3) --- 5 cases

Cases for total 7 - (1,6) (6,1) (4,3) (3,4) (2,5) (5,2) --- 6 cases

Total favourable cases will be 4 + 5 + 6 = 15

Total cases = 6**2 = 36

Probability = 15/36

3)

If die is rolled once, then output can be 1,2,3,4,5,6 and odd numbers in this list are 1,3,5 and the only number divisible by 3 is 3. Hence, there is only 1 such case out of 6.

Probability = 1/6

4)

If two dies are rolled and one number comes out to be 5, and we want sum more than 11, which is not possible as maximum number that can come out of the second die is 6 and the sum of both comes out to be 11.

Hence, probability, in this case, is 0.