In a play zone, Aastha is playing crane game. It has 12 blue balls, 8 red balls, 10 yellow balls and 5 green balls. If Aastha draws two balls one after the other without replacement, then answer the following questions.

(i) What is the probability that the first ball is blue and the second ball is green?

(ii) What is the probability that the first ball is yellow and the second ball is red?

(iii) What is the probability that both the balls are red?

(iv) What is the probability that the first ball is green and the second ball is not yellow?

(v) What is the probability that both the balls are not blue?

A doctor is to visit a patient. From the past experience, it is known that the probabilities that he will come by cab, metro, bike or by other means of transport are respectively 0.3, 0.2, 0.1 and 0.4. The probabilities that he will be late are 0.25, 0.3, 0.35 and 0.1 if he comes by cab, metro, bike and other means of transport respectively.

Based on the above information, answer the following questions.
(i) When the doctor arrives late, what is the probability that he comes by metro?

(ii) When the doctor arrives late, what is the probability that he comes by cab?

(iii) When the doctor arrives late, what is the probability that he comes by bike?

(iv) When the doctor arrives late, what is the probability that he comes by other means of transport?

(v) What is the probability that the doctor is late by any means?

On a holiday, a father gave a puzzle from a newspaper to his son Ravi and his daughter Priya. The probability of solving this specific puzzle independently by Ravi and Priya are \(\frac{1}{4}\) and \(\frac{1}{5}\) respectively.

Based on the above information, answer the following questions.
(i) The chance that both Ravi and Priya solved the puzzle, is

(ii) Probability that puzzle is solved by Ravi but not by Priya, is

(iii) Find the probability that puzzle is solved.

(iv) Probability that exactly one of them solved the puzzle, is

(v) Probability that none of them solved the puzzle, is

One day, a sangeet mahotsav is to be organised in an open area of Rajasthan. In recent years, it has rained only 6 days each year. Also, it is given that when it actually rains, the weatherman correctly forecasts rain 80% of the time. When it doesn't rain, he incorrectly forecasts rain 20% of the time.
If leap year is considered, then answer the following questions

(i) The probability that it rains on chosen day is

(ii) The probability that it does not rain on chosen day is

(iii) The probability that the weatherman predicts correctly is

(iv) The probability that it will rain on the chosen day, if weatherman predict rain for that day, is

(v) The probability that it will not rain on the chosen day, if weatherman predict rain for that day, is

To teach the application of probability a maths teacher arranged a surprise game for 5 of his students namely Archit, Aadya, Mivaan, Deepak and Vrinda. He took a bowl containing tickets numbered 1 to 50 and told the students go one by one and draw two tickets simultaneously from the bowl and replace it after noting the numbers.

Based on the above information, answer the following questions
(i) Teacher ask Vrinda, what is the probability that both tickets drawn by Archit shows even number?

(ii) Teacher ask Mivaan, what is the probability that both tickets drawn by Aadya shows odd number?

(iii) Teacher ask Deepak, what is the probability that tickets drawn by Mivaan, shows a multiple of 4 on one ticket and a multiple 5 on other ticket?

(iv) Teacher ask Archit, what is the probability that tickets are drawn by Deepak, shows a prime number on one ticket and a multiple of 4 on other ticket?

(v) Teacher ask Aadya, what is the probability that tickets drawn by Vrinda, shows an even number on first ticket and an odd' number on second ticket?