Probability
65 previous year questions.
High-Yield Trend
Chapter Questions 65 MCQs
On the basis of the above information, answer the following questions :
where is some unknown constant. The probability that the random variable takes the value 2 is:
The chances of , , and getting selected as CEO of a company are in the ratio , respectively. The probabilities for the company to increase its profits from the previous year under the new CEO , , or are , , and , respectively.
If the company increased the profits from the previous year, find the probability that it is due to the appointment of as CEO.
where is some unknown constant. The probability that the random variable takes the value 2 is:
Based upon the results of regular medical check-ups in a hospital, it was found that out of 1000 people, 700 were very healthy, 200 maintained average health and 100 had a poor health record.
Let : People with good health,
: People with average health,
and : People with poor health.
During a pandemic, the data expressed that the chances of people contracting the disease from category and are 25%, 35% and 50%, respectively.
Based upon the above information, answer the following questions:
(i) A person was tested randomly. What is the probability that he/she has contracted the disease?}
(ii) Given that the person has not contracted the disease, what is the probability that the person is from category ?
Reason (R): Two events are independent if the occurrence of one does not affect the occurrence of the other.
If and} , then is:
(i) The probability distribution of the number of oranges he draws.
(ii) The expectation of the number of oranges.
A shop selling electronic items sells smartphones of only three reputed companies A, B, and C because chances of their manufacturing a defective smartphone are only 5%, 4%, and 2% respectively. In his inventory, he has 25% smartphones from company A, 35% smartphones from company B, and 40% smartphones from company C.
A person buys a smartphone from this shop
(i) What is the probability that a customer after availing the loan will default on the loan repayment?
(ii) A customer after availing the loan, defaults on loan repayment. What is the probability that he availed the loan at a variable rate of interest?
A shop selling electronic items sells smartphones of only three reputed companies A, B, and C because chances of their manufacturing a defective smartphone are only 5%, 4%, and 2% respectively. In his inventory, he has 25% smartphones from company A, 35% smartphones from company B, and 40% smartphones from company C.
A person buys a smartphone from this shop
(i) Find the probability that it was defective.
(i) The probability that she buys both the colouring book and the box of colours.
(ii) The probability that she buys a box of colours given she buys the colouring book.
A gardener wanted to plant vegetables in his garden. Hence he bought 10 seeds of brinjal plant, 12 seeds of cabbage plant, and 8 seeds of radish plant. The shopkeeper assured him of germination probabilities of brinjal, cabbage, and radish to be 25%, 35%, and 40% respectively. But before he could plant the seeds, they got mixed up in the bag and he had to sow them randomly.
Calculate the probability of a randomly chosen seed to germinate.
Four students of class XII are given a problem to solve independently. Their respective chances of solving the problem are: Find the probability that at most one of them will solve the problem.
Probability Distribution of Random Variable X
| X | 1 | 2 | 3 | 2λ | 3λ | 4λ |
|---|---|---|---|---|---|---|
| P(X) |
(i) Calculate , if
(ii) Find P(X > 1).
Two persons are competing for a position on the Managing Committee of an organisation. The probabilities that the first and the second person will be appointed are 0.5 and 0.6, respectively. Also, if the first person gets appointed, then the probability of introducing a waste treatment plant is 0.7, and the corresponding probability is 0.4 if the second person gets appointed.
Based on the above information, answer the following
The probability distribution of a random variable is given below:
| 1 | 2 | 4 | 2k | 3k | 5k | |
(ii) Calculate the mean of the number of absent students on Saturday.
- Amber: 60%
- Bonzi: 30%
- Comet: 10%
- Amber: 20%
- Bonzi: 10%
- Comet: 5%
The probability of hitting the target by a trained sniper is three times the probability of not hitting the target on a stormy day due to high wind speed. The sniper fired two shots on the target on a stormy day when wind speed was very high. Find the probability that
(i) target is hit.
(ii) at least one shot misses the target. 
Smoking increases the risk of lung problems. A study revealed that 170 in 1000 males who smoke develop lung complications, while 120 out of 1000 females who smoke develop lung related problems. In a colony, 50 people were found to be smokers of which 30 are males. A person is selected at random from these 50 people and tested for lung related problems. Based on the given information answer the following questions: 
(i) What is the probability that selected person is a female?
(ii) If a male person is selected, what is the probability that he will not be suffering from lung problems?
(iii)(a) A person selected at random is detected with lung complications. Find the probability that selected person is a female.
OR
(iii)(b) A person selected at random is not having lung problems. Find the probability that the person is a male.