Tag: maths

Questions Related to maths

Two cards are drawn from a single deck of $52$ cards one after the other. Find the probability of selecting a king from the first card and queen from the second card.

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

  1. $\dfrac{1}{26}$

  2. $\dfrac{4}{52}$

  3. $\dfrac{16}{663}$

  4. $\dfrac{4}{663}$

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Correct Option: D
Explanation:

Probability of selecting a king in the first card is $\dfrac{4}{52}$. (Since $4$ kings in $52$ cards).

Probability of selecting a queen from the second card after the first card is drawn out is $\dfrac{4}{51}$. (Since $4$ queens in left over $51$ cards.
Now probability of selecting a king from the first card and queen from the second card is $\dfrac{4}{52}\times \dfrac{4}{51}=\dfrac{4}{663}$.
Hence, option D is correct.

Toss three fair coins simultaneously and record the outcomes. Find the probability of getting atmost one head in the three tosses.

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

  1. $\dfrac{1}{6}$

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

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

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

Show answer
Correct Option: C
Explanation:

Toss three fair coins simultaneously and record the outcomes.The sample space is HHH, HHT, HTH, HTT, THH, THT, TTH and TTT N=8

atmost one head in 4 events
the probability of getting atmost one head in the three tosses.$P(E)=\dfrac{4}{8}=\dfrac{1}{2}$

Which one of the following is correct?

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

  1. An event having no sample point is called an elementary event

  2. An event having one sample point is called an elementary event

  3. An event having two sample point is called an elementary event

  4. An event having many sample point is called an elementary event

Show answer
Correct Option: B
Explanation:

An elementary event is an event which contains only a single element in the sample space. So, it will have only $1$ sample point.
Hence, option B is true

Identify and write the like terms in each of the following groups.
(i) $ a^2, b^2, -2a^2 , c^2 , 4a$ 

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

  1. $(a^6,2a^2)$

  2. $(a^2,-2a^2)$

  3. $(a^3,2a^2)$

  4. $(a^2,2a^3)$

Show answer
Correct Option: B
Explanation:

In $a^{2},b^{2},-2a^{2},c^{2},4a.$

 $a^{2}$ and  $-2a^{2}$ are like terms because  $-2a^{2}$ is a factor of $a^{2}$ 
$B$ is correct.

$P\left(\dfrac{B}{ A}\right)$ is defined only when:

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

  1. $A$ is a sure event

  2. $B$ is a sure event

  3. $A$ is not an impossible event

  4. $B$ is an impossible event

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Correct Option: C
Explanation:

$P(\dfrac{B}{A})$ is the conditional probability of $B$ given $A$ or  it is the the probability of $B$ under the condition $A$, which is only possible if event $A$ occurs (i.e., $A$ is a possible event). 

$P(A/ B')$ is defined only when

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

  1. $B$ is not a sure event

  2. $B$ is a sure event

  3. $B$ is an impossible event

  4. $B$ is not an impossible event

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Correct Option: A
Explanation:

P(A/B) is the conditional probability of A given B or it is the probability of A under the condition B, which is only possible if event B occurs (i.e., B is a possible event). 

Similarly, P(A/B') is possible only when B' is sure or B is not sure.

If $P(A) = 1$, then the event $A$ is known as

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

  1. Symmetric event

  2. Dependent event

  3. Improbable event

  4. Sure event

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Correct Option: D
Explanation:

The probability is the possibility of an event happening when the probability of an event is 1, it means the event will occur for sure.

If $P(A) = 0$, then the event $A$

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

  1. Will never happen

  2. Will always happen

  3. May happen

  4. May not happen

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Correct Option: A
Explanation:

The probability is the possibility of an event happening when the probability of an event is zero, it means the event will never occur.

The probability of a sure event (or certain event) is ____

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

  1. $0$

  2. $1$

  3. $2$

  4. $3$

Show answer
Correct Option: B
Explanation:

Probability of event in $E$, $ P\left( E \right) =\dfrac { \text {number of events in E} }{ \text {Tota number of possible events} } $

If the number of desirable events is equal to the total number of possible events, then probability of an event which is certain or sure to happen $ = 1$
Such an event is called certaind event or sure event.

The probability of an event that is certain to happen is ____?

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

  1. $1$

  2. $2$

  3. $3$

  4. $4$

Show answer
Correct Option: A
Explanation:

The event that is sure to happen is called a certain event and probability of such an event is $1$ as this event is bound to happen.