Tag: events and its algebra

Questions Related to events and its algebra

The probability that an event does not happens in one trial is 0.8.The probability that the event happens atmost once in three trails is 

maths introduction of probability theory types of events some more terms in probability events and its algebra

  1. $0.896$

  2. $0.791$

  3. $0.642$

  4. $0.592$

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Correct Option: A

If for two events $A$ and $B, P(A\cap B)\ne P(A) \times P(B)$, then the two events $A$ and $B$ are

maths introduction of probability theory types of events some more terms in probability events and its algebra

  1. Independent

  2. Dependent

  3. Not equally likely

  4. Not exhaustive

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Correct Option: B
Explanation:

For independent.events $P\left( A\cap B \right) =P\left( A \right) .P\left( B \right) $

So, $P\left( A\cap B \right) \neq P\left( A \right) .P\left( B \right) $ implies that A and B are independent.

A bag contains four tickets marked with $112, 121, 211, 222$, one ticket is drawn at random from the bag. Let $E _i(i=1, 2, 3)$ denote the event that $i^{th}$ digit on the ticket is $2$ then :

maths introduction of probability theory types of events some more terms in probability events and its algebra

  1. $E _1$ and $E _2$ are independent

  2. $E _2$ and $E _3$ are independent

  3. $E _3$ and $E _1$ are independent

  4. $E _1, E _2, E _2$ are independent

Show answer
Correct Option: A,B,C
Explanation:

$P(E _1) = P(E _2) = P(E _3) =\dfrac{1}{2}$


$P(E _i \cap E _j) = \dfrac{1}{4} = P(E _i)P(E _j)$

Hence, two events taken together are independent.

$P(E _1 \cap E _2 \cap E _3) = \dfrac{1}{4} \neq P(E _1)P(E _2)P(E _3)$

Therefore, the three events are not independent together.

Hence, options A, B and C are correct.

Two cards are drawn simultaneously from a well shuffled pack of $52$ cards. The expected number of aces is?

maths introduction of probability theory types of events some more terms in probability events and its algebra

  1. $\dfrac{1}{221}$

  2. $\dfrac{3}{131}$

  3. $\dfrac{2}{113}$

  4. $\dfrac{1}{131}$

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Correct Option: A
Explanation:

$\begin{matrix} Two\, \, cards\, \, are\, \, drawn\, \, from\, \, a\, \, well\, \, shuffered\, \, pack\, \, of\, \, 52\, \, card. \ Then,\, \, number\, \, access\, \, is\, \,  \ \Rightarrow number\, \, of\, \, sample\, \, space=52/2 \ \Rightarrow There\, \, are\, \, four\, \, ace=\dfrac { { 4/2 } }{ { 52/2 } } =\frac { { 4\times 3 } }{ { 52\times 51 } }  \ =\dfrac { 1 }{ { 13\times 17 } } \, \, \, \, \, Ans. \  \end{matrix}$

Probability of any event $x$ lies

maths introduction of probability theory types of events some more terms in probability events and its algebra

  1. $0 < x < 1$

  2. $0\leq x < 1$

  3. $0\leq x \leq 1$

  4. $1 < x < 2$

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Correct Option: C
Explanation:

$P\in \left [ 0,1 \right ]$ 


Option $(C)$ is correct.

Probability of impossible event is

maths introduction of probability theory types of events some more terms in probability events and its algebra

  1. $1$

  2. $0$

  3. $\dfrac {1}{2}$

  4. $-1$

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Correct Option: B
Explanation:

(P) Of possible event is $0$

Which one can represent a probability of an event

maths introduction of probability theory types of events some more terms in probability events and its algebra

  1. $\dfrac {7}{4}$

  2. $-1$

  3. $-\dfrac {2}{3}$

  4. $\dfrac {2}{3}$

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Correct Option: D
Explanation:

     $P <  1$


 Optoion (D) is correct $2/3$

Probability of sure event is

maths introduction of probability theory types of events some more terms in probability events and its algebra

  1. $1$

  2. $0$

  3. $\dfrac {1}{2}$

  4. $2$

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Correct Option: A
Explanation:

Probability of sure event is always $1$

If P(A) = P(B), then

maths introduction of probability theory types of events some more terms in probability events and its algebra

  1. A and B are the same events

  2. A and B must be same events

  3. A and B may be different events

  4. A and B are mutually exclusive events.

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Correct Option: C
Explanation:
Given $P(A) = P(B)$
Then $A$ can be different event from $B$ because $A\;\xi\;B$ are Mutually exclusive.
i.e, $A\;\xi\;B$ may be different events.
Hence, the answer is $A$ and $B$ may be different events.

In a single throw of die, what is the probability of getting a number greater than 3 ?

maths introduction of probability theory types of events some more terms in probability events and its algebra

  1. $\dfrac12$

  2. $\dfrac23$

  3. $\dfrac13$

  4. none of these

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Correct Option: A