11th Maths Weekly Test - 4 ( Introduction to probability theory )

St. Britto Hr. Sec. School - Madurai

11th Maths Weekly Test - 4 ( Introduction to probability theory )-Aug 2020

Time : 1.30 Hours

Part - A

Generic 3 - Answer All Question

A basket contains 20 apples and 10 oranges out of which 5 apples and 3 oranges are defective. If a person takes out 2 at random what is the probability that either both are apples or both are good?

A problem in Mathematics is given to three students whose chances of solving A problem in Mathematics is given to three students whose chances of solving \(\frac { 1 }{ 3 } ,\frac { 1 }{ 4 } \) and \(\frac { 1 }{ 5 } \) (i) What is the probability that the problem is solved? (ii) What is the probability that exactly one of them will solve it?

The chances of A, B, and C becoming manager of a certain company are 5 : 3: 2. The probabilities that the office canteen will be improved if A, B, and C become managers are 0.4, 0.5 and 0.3 respectively. If the office canteen has been improved, what is the probability that B was appointed as the manager?

The probability that a girl, preparing for competitive examination will get a State Government service is 0.12, the probability that she will get a Central Government job is 0.25, and the probability that she will get both is 0.07. Find the probability that (i) she will get atleast one of the two jobs (ii) she will get only one of the two jobs.

Suppose a fair die is rolled. Find the probability of getting
(i) an even number (ii) multiple of three

The probability that a car being filled with petrol will also need an oil change is 0.30; the probability that it needs a new oil filter is 0.40; and the probability that both the oil and filter need changing is 0.15.
(i) If the oil had to be changed, what is the probability that a new oil filter is needed?
(ii) If a new oil filter is needed, what is the probability that the oil has to be changed

Let the matrix M=\(\left[ \begin{matrix} x & y \\ z & 1 \end{matrix} \right] \), If x,y and z are chosen at random from the set {1, 2,3, } and repetition is allowed (i.e., x=y=z ), what is the probability that the given matrix M is a singular matrix?

If A and B are mutually exclusive events P(A)=\(\frac{3}{8}\) and P(B)=\(\frac{1}{8}\) , then find
(i) P(\(\bar { A } \))
(ii) \(P(A\cup B)\)
(iii) \(P(\bar { A } \cap B)\)
(iv) \(P(\bar { A } \cup \bar { B } )\)

A persons 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 no 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 die is thrown twice. Let A be the event, ‘First die shows 5’ and B be the event 'second die shows 5’. Find \(P(A\cup B)\) .

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11th Maths Weekly Test - 4 ( Introduction to probability theory )

St. Britto Hr. Sec. School - Madurai

11th Maths Weekly Test - 4 ( Introduction to probability theory )-Aug 2020

Part - A

Generic 3 - Answer All Question

A basket contains 20 apples and 10 oranges out of which 5 apples and 3 oranges are defective. If a person takes out 2 at random what is the probability that either both are apples or both are good?

Suppose a fair die is rolled. Find the probability of getting (i) an even number (ii) multiple of three

Let the matrix M=\(\left[ \begin{matrix} x & y \\ z & 1 \end{matrix} \right] \), If x,y and z are chosen at random from the set {1, 2,3, } and repetition is allowed (i.e., x=y=z ), what is the probability that the given matrix M is a singular matrix?

If A and B are mutually exclusive events P(A)=\(\frac{3}{8}\) and P(B)=\(\frac{1}{8}\) , then find (i) P(\(\bar { A } \)) (ii) \(P(A\cup B)\) (iii) \(P(\bar { A } \cap B)\) (iv) \(P(\bar { A } \cup \bar { B } )\)

A die is thrown twice. Let A be the event, ‘First die shows 5’ and B be the event 'second die shows 5’. Find \(P(A\cup B)\) .

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Suppose a fair die is rolled. Find the probability of getting
(i) an even number (ii) multiple of three

If A and B are mutually exclusive events P(A)=\(\frac{3}{8}\) and P(B)=\(\frac{1}{8}\) , then find
(i) P(\(\bar { A } \))
(ii) \(P(A\cup B)\)
(iii) \(P(\bar { A } \cap B)\)
(iv) \(P(\bar { A } \cup \bar { B } )\)