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

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.

  1. $\dfrac{1}{26}$
  2. $\dfrac{4}{52}$
  3. $\dfrac{16}{663}$
  4. $\dfrac{4}{663}$
Reveal answer Fill a bubble to check yourself
D Correct answer
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.

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

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

  1. $\dfrac{1}{6}$
  2. $\dfrac{1}{4}$
  3. $\dfrac{1}{2}$
  4. $\dfrac{1}{3}$
Reveal answer Fill a bubble to check yourself
C Correct answer
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.$P(E)=\dfrac{4}{8}=\dfrac{1}{2}$

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

Which one of the following is correct?

  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
Reveal answer Fill a bubble to check yourself
B Correct answer
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

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

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

  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
Reveal answer Fill a bubble to check yourself
C Correct answer
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). 

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

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

  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
Reveal answer Fill a bubble to check yourself
A Correct answer
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.

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

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

  1. $0$
  2. $1$
  3. $2$
  4. $3$
Reveal answer Fill a bubble to check yourself
B Correct answer
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.