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11th Maths Weekly Test - 1 ( Introduction to probability theory )

St. Britto Hr. Sec. School - Madurai

11th Maths Weekly Test - 1 ( Introduction to probability theory )-Aug 2020

Time : 1.30 Hours

Part - A

Multiple Choice Question - Answer All Question

A die is thrown and a card is selected at random from a deck of 52 playing cards. The probability of getting an even number of the die and a spade card is

\(\frac { 1 }{ 2 } \)
\(\frac { 1 }{ 4 } \)
\(\frac { 1 }{ 8 } \)
\(\frac { 3 }{ 4 } \)

If A and B are two independent events with P(A) = \(\frac { 3 }{ 5 } \) and P(B)=\(\frac { 4 }{ 9 } \) then \(P(\bar { A } \cap \bar { B } )\) = equals

\(\frac { 4 }{ 15 } \)
\(\frac { 8 }{ 45 } \)
\(\frac { 1 }{ 3 } \)
\(\frac { 2 }{ 9 } \)

if A and B are two events, the \(P(\bar { A } \cap B)\) =

\(P\left( \bar { A } \right) .P(\bar { B } )\)
1-P(A)-P(B)
P(A)+P(B)-P(A\(\cap \)B)
P(B)-P(A\(\cap \) B)

If P(A)=\(\frac { 1 }{ 2 } \), P(B)=\(\frac { 1 }{ 3 } \) and P(A/B) = \(\frac { 1 }{ 4 } \), then \(P(\bar { A } \cap \bar { B } )\) =

\(\frac { 1 }{ 12 } \)
\(\frac { 3 }{ 4 } \)
\(\frac { 1 }{ 4 } \)
\(\frac { 3 }{ 16 } \)

Four persons are selected at random from a group of 3 men, 2 women, and 4 children. The probability that exactly two of them are children is

\({3\over4}\)
\({10\over23}\)
\({1\over2}\)
\({10\over21}\)

A flash light has 8 batteries out of which 3 are dead. If 2 batteries are selected without replacement and tested, the probability that both are dead is

\(\frac { 3 }{ 28 } \)
\(\frac { 1 }{ 14 } \)
\(\frac { 9 }{ 64 } \)
\(\frac { 33 }{ 56 } \)

If two events A and B are independent such that P(A)=0.35 and \(P(A\cup B)=0.6\) ,then P(B) is

\({5\over 13}\)
\({1\over 13}\)
\({4\over 13}\)
\({7\over 13}\)

If A and B are two events such that \(P(A\cap B)=\frac { 7 }{ 10 } \) and P(B) = \(\frac { 17 }{ 20 } \) , then P(A/B) =

\(\frac { 14 }{ 17 } \)
\(\frac { 17 }{ 20 } \)
\(\frac { 7 }{ 8 } \)
\(\frac { 1 }{ 8 } \)

Let A and B be two events such that \(P(\overline{A\cup B})={1\over6}, P(A\cap B)={1\over4}\) and \({P(\overline{A})}={1\over4}\). Then the events A and B are

Equally likely but not independent
Independent but not equally likely
Independent and equally likely
Mutually inclusive and dependent

If A and B are any two events, then the probability that exactly one of them occur is

\(P(A\cup\overline{B})+P(\overline{A}\cup B)\)
\(P(A\cap\overline{B})+P(\overline{A}\cap B)\)
\(P(A)+P({B})-P({A}\cap B)\)
\(P(A)+P({B})+2P({A}\cap B)\)

Part - B

Generic 2 - Answer All Question

An experiment has the four possible mutually exclusive and exhaustive outcomes A, B, C, and D. Check whether the following assignments of probability are permissible
P(A) = 0.15, P(B) = 0.30, P(C) = 0.43 , P(D)= 0.12

If an experiment has exactly the three possible mutually exclusive outcomes A, B, and C, check in each case whether the assignment of probability is permissible
\(P(A)=0.3,P(B)=0.9,P(C)=-0.2\)

A die is tossed thrice. find the probability of getting an odd number atleast once?
Find the probability of getting the number 7, when a usual die is rolled

Given that P(A) =0.52, P(B)=0.43, and P(A∩B)=0.24, find
P\(\left( \overline { A } \cap \overline { B } \right) \)

Part - C

Generic 3 - Answer All Question

A firm manufactures PVC pipes in three plants viz, X, Y, and Z. The daily production volumes from the three firms X, Y and Z are respectively 2000 units, 3000 units, and 5000 units. It is known from the past experience that 3% of the output from plant X, 4% from plant Y and 2% from plant Z are defective. A pipe is selected at random from a day’s total production,
(i) find the probability that the selected pipe is a defective one.
(ii) if the selected pipe is a defective, then what is the probability that it was produced by plant Y?

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?

A and B are two events such that P(A) \(\neq \) 0. Find P(B/A) if (i) A is a subset of B (ii) A\(\cap \)B = \(\phi \)

A town has 2 fire engines operating independently. The probability that a fire engine is available when needed is 0.96.
(i) What is the probability that a fire engine is available when needed?
(ii) What is the probability that neither is available when needed?

Part - D

Generic 5 - Answer All Question

A year is selected at random. What is the probability that
(i) it contains 53 Sundays
(ii) it is a leap year which contains 53 Sundays.

Suppose ten coins are tossed. Find the probability to get (i) exactly two heads (ii) at most two heads (iii) at least two heads

The probability of simultaneous occurrence of atleast one of two events A and B is p. if the probability that exactly one A, B occurs is q then prove that P(\(\bar { A } \)) + P(\(\bar { B } \)) = 2-2 p+q.
When a pair of fair dice is rolled, what are the probabilities of getting the sum
(i)7
(ii) 7 or 9
(iii) 7 or 12?

If A and B are two independent events such that P(A\(\cup \)B)=0.6, P(A)=0.2, find P(B).

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