Mathematics · JEE

Probability: Probability of an event, addition and multiplication theorems of probability Mock Test for JEE

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Syllabus context

Part of Statistics and Probability in JEE Main Mathematics.

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Q1MathsUnit 13: Statistics and Probability

The probability of an even happens in one trial of an experiment is

0.3 .

Three independent trials of the experiments are performed. Find the probability that the event A happens at least once.

Q2MathsUnit 13: Statistics and Probability

A

and

B

are independent events such that

\mathbf{0}<\boldsymbol{P}(\boldsymbol{A})<\mathbf{1}, \mathbf{0}<\boldsymbol{P}(\boldsymbol{B})<\mathbf{1},

then This question has multiple correct options

Q3MathsUnit 13: Statistics and Probability

Mr. Dixit resigned from the company after 4 years of service.

Q4MathsUnit 13: Statistics and Probability

For two events

A

and

B

, if

P(A)=

\boldsymbol{P}(\boldsymbol{A} \mid \boldsymbol{B})=\mathbf{1} / \mathbf{4}

and

\boldsymbol{P}(\boldsymbol{B} \mid \boldsymbol{A})=\mathbf{1} / 2,

then This question has multiple correct options

Q5MathsUnit 13: Statistics and Probability

What is the probability of selecting two spade cards from a pack of 52 cards?

Q6MathsUnit 13: Statistics and Probability

\boldsymbol{P}(\boldsymbol{A})=\boldsymbol{P}(\boldsymbol{B}),

then the two events

\boldsymbol{A}

and

B

are -

Q7MathsUnit 13: Statistics and Probability

A manufactacturer buys raw material for Rs. 60,000 and pays

4 \%

tax. He sells the ready stocks for Rs. 92,000 and charges

12.5 \%

tax. Find the VAT paid by the manufacturer.

Q8MathsUnit 13: Statistics and Probability

The length of life of an instrument produced by a machine has a normal distribution with a mean of 12 months and standard deviation of 2 months. Find the probability that an instrument produced by this machine will last less than 7 months.

Q9MathsUnit 13: Statistics and Probability

A fair die is tossed 1620 times. If getting a face with 6 points is considered as a success, then

E(x)=

\ldots \ldots ., V(x)=\dots \ldots . .

Q10MathsUnit 13: Statistics and Probability

Choosing a marble from a jar and landing on heads after tossing a coin is an act of

Q11MathsUnit 13: Statistics and Probability

Let

A

and

B

be two events such that

P(\overline{A \cup B})=\frac{1}{6}, P(A \cap B)=\frac{1}{4}

and

P(\bar{A})=\frac{1}{4},

where

\bar{A}

stands for the complement of the event A. Then the events

A

and

B

are?

Q12MathsUnit 13: Statistics and Probability

When a coin is tossed at random, then the probability of getting a head is

Q13MathsUnit 13: Statistics and Probability

A machine has three parts,

A, B

and

C

whose chances of being defective are 0.02,0.10 and 0.05 respectively. The machine stops working if any one of the arts becomes defective. What is the probability that the machine will not stop working?

Q14MathsUnit 13: Statistics and Probability

A

and

B

are two events where

P(A)=

0.25 and

P(B)=0.5 .

The probability of both happening together is 0.14 . The probability of both

A

and

B

not happening is

Q15MathsUnit 13: Statistics and Probability

The probability that atleast one of the events

A, B

happens is

0.6 .

If probability of their simultaneously happening is

0.5,

then

\boldsymbol{P}(\overline{\boldsymbol{A}})+\boldsymbol{P}(\overline{\boldsymbol{B}})=

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