Two buses A and B are scheduled to arrive at a town central bus station at noon. The probus A will be late is `1/5`. The probability that bus B will be late is `7/25`. The probability that the bus B is late given that bus A is late is `9/10`. Then the probabilities: neither bus will be late on a particular day.

The probability that married man watches certain TV show is 0.4 and the probabi9lity that a married woman watches the show is 0.5. the probability that a man watches the show, given that his wife dies, is 0.7. then (a)the probability that married couple watches the show is 0.35 (b)the probability that a wife watches the show given that her husband does is 7/8 (c)the probability that at least one person of a married couple will watch the show is 0.55 (d)none of these

Two events A and B have probabilities 0.25 and 0.5, respectively. The probability that both A and B occur simultaneously is 0.14. then the probability that neither A nor B occurs is (A) 0.39 (B) 0.25 (C) 0.11 (D) none of these

The probability that a marksman will hit a target is given is 1/5. Then the probability that at least once hit in 10 shots is a. 1-(4//5)^(10) b. 1//5^(10) c. 1-(1//5)^(10) d. (4//5)^(10)

A die is thrown a fixed number of times. If probability of getting even number 3 times is same as the probability of getting even number 4 times, then probability of getting even number exactly once is a. 1//6 b. 1//9 c. 5//36 d. 7//128

Two numbers a ,b are chosen from the set of integers 1, ,2 3, ..., 39. Then probability that he equation 7a-9b=0 is satisfied is 1//247 b. 2//247 c. 4//741 d. 5//741

There are some experiment in which the outcomes cannot be identified discretely. For example, an ellipse of eccentricity 2sqrt(2)//3 is inscribed in a circle and a point within the circle is chosen at random. Now, we want to find the probability that this point lies outside the ellipse. Then, the point must lie in the shaded region shown in Figure. Let the radius of the circle be a and length of minor axis of the ellipse be 2b. Given that 1 - (b^(2))/(a^(2)) = (8)/(9) or (b^(2))/(a^(2)) = (1)/(9) Then, the area of circle serves as sample space and area of the shaded region represents the area for favorable cases. Then, required probability is p= ("Area of shaded region")/("Area of circle") =(pia^(2) - piab)/(pia^(2)) = 1 - (b)/(a) = 1 - (1)/(3) = (2)/(3) Now, answer the following questions. Two persons A and B agree to meet at a place between 5 and 6 pm. The first one to arrive waits for 20 min and then leave. If the time of their arrival be independant and at random, then the probability that A and B meet is

A six-faced dice is so biased that it is twice as likely to show an even number as an odd number when thrown. It is thrown twice, the probability that the sum of two numbers thrown is even is a. 1//12 b. 1//6 c. 1//3 d. 5//9

A person goes to office either by car, scooter, bus or train probability of which being 1/7, 3/7, 2/7 and 1/7 respectively. Probability that he reaches office late, if he takes car, scooter, bus or train is 2/9, 1/9, 4/9 and 1/9 respectively. Given that he reached office in time, then what is the probability that he travelled by a car?

A signal which can be green or red with probability 4/5 and 1/5 respectively, is received by station A and then and 3 transmitted to station B. The probability of each station receiving the signal correctly is 3/4 If the signal received at station B is green, then the probability that the original signal was green is (a) 3/5 (b) 6/7 (c) 20/23 (d) 9/20