Tag: mathematics and statistics

Quizzes (38) Questions (955)

Questions Related to mathematics and statistics

Multiple choice mathematics and statistics set language de morgan's law for set theory complement of sets different sets de morgan's law

If $A$ and $B$ are subsets of $U$ such that $n(U) = 700, n(A) = 200, n(B) = 300, n$$\displaystyle \left ( A\cap B \right )$ $= 100$, then find $n\displaystyle \left ( A'\cap B' \right )$

  1. $405$
  2. $305$
  3. $400$
  4. $300$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

We know that $\displaystyle \left ( A\cup B \right )'=$ $\displaystyle A'\cap B'$ so we need to find $\displaystyle \left ( A\cup B \right ) $  first.
$n\displaystyle \left ( A\cup B \right ) =$ $n(A) + n(B) - n$$\displaystyle (A\cap B)$ $= 200 + 300 - 100 = 400$
$n\displaystyle \left ( A\cup B \right )' =$ $n(U) - n$$\displaystyle \left ( A\cup B \right )'=$$  700 - 400 = 300$
$\displaystyle \Rightarrow $ $n\displaystyle (A'\cap B')$$= 300$.

Multiple choice mathematics and statistics set language de morgan's law for set theory complement of sets different sets de morgan's law

If A has 5 elements and B has 8 elements such that $\displaystyle A\subset B,$ then the number of elements in $\displaystyle A\cap  B,$ and $\displaystyle A\cup  B,$ are respectively :

  1. 8 , 5

  2. 3 , 3

  3. 5, 8

  4. 5, 13
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Since $A\subset B$, $A\cap B$ will be all the elements of A. So, the number of elements will be 5.
Since $A\subset B$, $A\cup B$ will be all the elements of A & B. So, the number of elements will be 8.

Multiple choice mathematics and statistics set language de morgan's law for set theory complement of sets different sets de morgan's law

While preparing the progress reports of the students, the class teacher found that $70$% of the students passed in Hindi, $80$% passed in English and only $65$% passed in both the subjects. Find out the percentage of students who failed in both the subjects

  1. $15$%
  2. $20$%
  3. $30$%
  4. $35$%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Students passed in Hindi $ = 70\% =n(H)$

Students passed in English $ = 80\% =n(E)$

Students passed in Both $ = 65\% =n(H\cap E)$

No. of students passed $=n(H \cup E)= n(H)+n(E)-n(H \cap E) = 70+80-65 =85\%$

No. of Students failed $= 100\% - n(H \cup E) = 100\% - 85\% = 15\%$

Multiple choice mathematics and statistics set language de morgan's law for set theory complement of sets different sets de morgan's law

In a science talent examination, $50$% of the candidates fail in Mathematics and $50$% fail in Physics. If $20$% fail in both these subjects, then the percentage who pass in both Mathematics and Physics is

  1. $0$%
  2. $20$%
  3. $25$%
  4. $50$%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Fail: $n(M) =50\%$

$n(P) =50\%$

$n(M \cap P) =20\%$

$n(M\cup P) =n(M)+n(P)-n(M\cap P)$

$n(M\cup P) =50+50-20 = 80\%$

Pass:

n(Pass in both subjects) $=100\%$ -n(Fail in both the subjects)

$=100\% -80\% = 20\%$

Multiple choice mathematics and statistics set language de morgan's law for set theory complement of sets different sets de morgan's law

In a survey, it was fond that $65$% of the people watched news on TV, $40$% read in newspaper, $25$% read newspaper and watched TV. What percentage of people neither watched TV nor read newspaper?

  1. $0$%
  2. $5$%
  3. $10$%
  4. $20$%
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

n(Watch new on TV) $=65\%=n(T)$

n(Reads newspaper) $=40\%=n(N)$

n(Watch news on TV & read newspapers ) $=25\%=n(T\cap N)$

$n(N \cup T)= n(T)+n(N)-n(N\cap T)$

$n(N \cup T)= 65+40-25 = 80\%$

$n(N\cap T)^{c}=100-80=20\%$