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A pair of dice is thrown. If the two numbers appearing on them are different, find the probability (i) the sum of the numbers is 6(ii) the sum of the numbers is 4 or less (iii) the sum of the number is 4.
An electronic assembly consists of two sub-system, say A and B. From previous testing procedures, the following probabilities are assumed to be known.
P(A fails) = 0.2, P(B fails alone) = 0.15, P(A and B fail) = 0.15
Evaluate the following probabilities:
(i) P(A fails/B has failed)
(ii) P (A fails alone)
Two balls are drawn from an urn containing 2 white, 3 red and 4 black balls one by one without replacement. What is the probability that at least one balls is red?
The odds against A solving a certain problem are 4 to 3 and the odds in favour of B solving the same problem are 7 to 5. Find the probability that the problem will be solved.
Mother, father and son line up at random for a family picture. Find P(A/B), if A and B are defined as follows:
A = Son on one end, B = Father in the middle
A die is thrown three times. Events A and B are defined as follows:
A: 4 on the third throw; B: 6 on the first and 5 on the second throw.
Find the probability of A given that B has already occurred.
A couple has 2 children. Find the probability that both are boys, if it is known that (i) one of the children is a boy: (ii) the older child is a boy.
A, B and C shot to hit a target. If A hits the target 4 times in 5 trials; B hits it 3 times in 4 trails and C hits 2 times in 3 trials; what is the probability that the target is hit by a least 2 persons?
Three persons, A, B, C throw a die in succession till one gets a ‘six’ and wins the game. Find their respective probabilities of winning, if A begins.
One bag contains 4 white and 5 black balls. Another bag contains 6 white and 7 black balls. A ball is transferred form first bag to the second bag and then a ball is drawn from the second bag. Find the probability that the ball drawn is white.
Two persons A and B throw a die alternately till one of them gets a ‘three’ and wins the game. Find their respectively probabilities of wining, if A begins.
The probabilities of A, B, C solving a problem are 1/3, 2/7 and 3/8 respectively. If all the three try to solve the problem simultaneously, find the probability that exactly one of them can solve it.
In a bolt factory, machines A, B and C manufacture respectively, 25%, 35% and 40% of the total bolts. Of their output 5, 4, and 2 percent are respectively defective bolts. A bolt is drawn at random from the product. If the bolt drawn is found to be defective, what is the probability that it is manufactured by the machine B?
A person has undertaken a construction job. The probabilities are 0.65 that there will be strike, 0.80 that the construction job will be completed on time if there is not strike, and 0.32 that the construction job will be completed on time if there is a strike. Determine the probability that the construction job will be completed on time.
A bag contains 4 red and 3 black balls. A second bag contains 2 red and 4 black balls. One bag is selected at random. From the selected bag, one ball is drawn. Find the probability that the ball drawn is red.
A and B throw alternately a pair of dice. A wins if he throws 6 before B throws 7 and B wins if the throws 7 before A throws 6. Find their respective chance of winning, if A begins.
A speaks truth in 60% of the cases and B in 90% of the cases. In what percentage of cases are they likely to contradict each other in stating the same fact?
A can hit a target 4 times in 5 shots, B 3 times in 4 shots, and C 2 times in 3 shots. Calculate the probability that
(i) A, B, C all may hit
(ii) B, C may hit and A may lose
(iii) any two of A, B and C will hit the target.
(iv) none of them will hit the target.
If each element of a second order determinant is either zero or one, what is the probability that the value of the determinant is positive? (Assuming that the individual entries of the determinant are chose independently, each value being assumed with probability 1/2).
If each element of a second order determinant is either zero or one, what is the probability that the value of determinant is non-negative?