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GATE20 Engg. Mathematics Series: Probability Quiz 2 (App update required to attempt this test)
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Question 1
If a dice is thrown, _______ is the probability of occurrence of a number greater than 1, when it is known that only odd numbers can come up.
Question 2
A bolt is manufactured by 3 machines A, B and C. Machine A turn out twice as many items as B, and machines B and C produce equal number of items. 2% of bolts produced by A and B are defective and 4% of bolts produced by C are defective. All bolts put into 1 stock pile and 1 is chosen from this pile. The probability that it is defective is __________ x 10-1.
Question 3
A fair six sided die is thrown twice. If the sum of the face values of these two tosses is 5 then what is the probability that the face value of the first toss is less than that of second toss?
Question 4
Box P has 2 red balls and 3 blue balls and box Q has 3 red balls and 1 blue ball. A ball is selected as follows:
(i) Select a box
(ii) Choose a ball from the selected box such that each ball in the box is equally likely to be chosen. The probabilities of selecting boxes P and Q are (1/3) and (2/3), respectively. Given that a ball selected in the above process is a red ball, the probability that it came from the box P is
(i) Select a box
(ii) Choose a ball from the selected box such that each ball in the box is equally likely to be chosen. The probabilities of selecting boxes P and Q are (1/3) and (2/3), respectively. Given that a ball selected in the above process is a red ball, the probability that it came from the box P is
Question 5
A box contains 4 bad and 6 good tubes. Two tubes are drawn at a time from the box.The first tube found out to be good, then probability that the other one is also good is
Question 6
Consider two bags B1 (6 Red and 5 Blue balls) and B2 (7 Red and 3 Blue Balls). A person takes a ball from bag B1 and placed it into B2 and finally choose a ball from bag B2. What is the probability that ball chosen is red___________(Round upto 3 decimal places).
Question 7
Urn 1 has five white and seven black balls. Urn 2 has three white and twelve black balls. We flip a fair coin. If the outcome is heads, then a ball from urn 1 is selected, while if the outcome is tails, then a ball from urn 2 is selected. Suppose that a white ball is selected. What is the probability that the coin landed tails______________ (round upto 2 decimal places).
Question 8
Suppose we are provided with two types of batteries, C & D. It is not guaranteed that the battery will surely work. Type C battery is in working condition with the probability of 0.7, whereas a type D battery is in working condition with the probability of 0.4. A battery is randomly chosen from a bin consisting of 8 type C and 6 type D batteries. Let ‘a’ be the probability that the battery will surely work, and 'b' be the probability that the chosen battery is of C type given that the battery doesn’t work. The value of a-b is_____________________.( round up to 2 decimal places)
Question 9
A survey was conducted in a region which showed that 25% drank regularly. The probability of death because of liver disease, given that a person drank regularly, was 6 times the probability of death due to liver disease, given that a person did not drink regularly. The probability of death due to liver disease in the region is 0.005. If a person dies due to liver disease what is the probability that he/she drank regularly?
Question 10
Let A, B , C be three events such that :
is __________
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