Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.

Probability

Long Answer Type

871.
The probability of A solving a problem is $3 over 7$ and that of B solving it is $1 third.$ What is the probability that
(i) at least one of them will solve the problem?
(ii) Only one of them will solve the problem?

Let E denote the event ‘A solves the problem’ and F denote the event ‘B solves the problem’.

therefore space space space space space space space straight P left parenthesis straight E right parenthesis space equals space 3 over 7 comma space space space straight P left parenthesis straight F right parenthesis space equals space 1 third therefore space space space space space space space straight P left parenthesis straight E with bar on top right parenthesis space equals space 1 space minus space straight P left parenthesis straight E right parenthesis space equals space 1 minus 3 over 7 space equals 4 over 7 space space space space space space space space space space space straight P left parenthesis straight F with bar on top right parenthesis space equals space 1 space space minus space straight P left parenthesis straight F right parenthesis space equals space 1 minus 1 third space equals 2 over 3

(i) P(none of them solves the problem) =

straight P space open parentheses straight E with rightwards arrow on top space and space straight F with rightwards arrow on top close parentheses

equals space straight P open parentheses straight E with rightwards arrow on top close parentheses space cross times space straight P open parentheses straight F with rightwards arrow on top close parentheses space equals space 4 over 7 cross times 2 over 3 space equals 8 over 21.

therefore space space space space space space straight P left parenthesis at space leastl space one space of space them space solves space the space problem right parenthesis

equals space 1 space minus straight P left parenthesis none space of space them space solves space the space problem right parenthesis space equals space 1 minus 8 over 21 space equals 13 over 21

(ii) P(only one solves the problem) =

straight P open parentheses apostrophe straight E space and space straight F with bar on top apostrophe space or space apostrophe straight E with bar on top space and space straight F apostrophe close parentheses

equals space straight P left parenthesis straight E space and space straight F with bar on top right parenthesis space plus space open parentheses straight E with bar on top space and space straight F with bar on top close parentheses equals space straight P left parenthesis straight E right parenthesis thin space straight P space open parentheses straight F with bar on top close parentheses space plus space straight P space open parentheses straight E with bar on top close parentheses space space straight P left parenthesis straight F right parenthesis space equals space 3 over 7 cross times 2 over 3 plus 4 over 7 cross times 1 third space equals 6 over 21 plus 4 over 21 space equals 10 over 21

86 Views

Short Answer Type

872. A speaks truth in 60% cases and B in 90% cases. In what percentage of cases are they likely to contradict each other in stating the same fact.

87 Views

873. A speaks truth in 75% and B in 80% of the cases. In what percentage of cases are they likely to contradict each other in narrating the same incident?

115 Views

874. The probability of hitting a target by three marksmen are

1 half comma space 1 third space and space 1 fourth

respectively. Find the probability that one and only one of them will hit the target when they fire simultaneously.

83 Views

875. An anti-aircraft gun can take a minimum of four shots at an enemy plane moving away from it. The probability of hitting the plane at the first, second, third and fourth shot are 0.4, 0.3, 0.2 and 0.1 respectively. What is the probability that the gun hits the plane?

125 Views