Tag: maths

Questions Related to maths

A pot has $2$ white, $6$ black, $4$ grey and $8$ green balls. If one ball is picked randomly from the pot, what is the probability of it being black or green?

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

  1. $\dfrac34$

  2. $\dfrac1{10}$

  3. $\dfrac43$

  4. $\dfrac7{10}$

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Correct Option: D

$10$ books are placed at random in a shelf. The probability that a pair of books will always be together is 

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

  1. $\dfrac1{5}$

  2. $\dfrac9{10}$

  3. $\dfrac1{10}$

  4. $\dfrac3{10}$

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Correct Option: A

A basket contains $6$ blue, $2$ red, $4$ green and yellow balls. If three balls are picked up at random, what is the probability that none is yellow ?

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

  1. $\dfrac{3}{455}$

  2. $\dfrac{1}{5}$

  3. $\dfrac{4}{5}$

  4. $\dfrac{44}{91}$

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Correct Option: D

Successive trials in binomial distribution are

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

  1. Dependent

  2. Independent

  3. Equally Likely

  4. Mutually exclusive

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Correct Option: B

The probability that A speaks truth is $\dfrac35$ and that of B speaking truth is $\dfrac47$. What is the probability that they agree in stating the same fact?

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

  1. $\dfrac {18}{35}$

  2. $\dfrac {12}{35}$

  3. $\dfrac {17}{35}$

  4. $\dfrac {19}{35}$

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Correct Option: A

If the occurrence of one event means that another cannot happen, then the events are

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

  1. Bayesian

  2. Empirical

  3. Independent

  4. Mutually Exclusive

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Correct Option: D

The probability of success of three students X,Y and Z in the one examination are $\dfrac15, \dfrac14$ and $\dfrac13$ respectively. Find the probability of success of at least two.

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

  1. $\dfrac16$

  2. $\dfrac25$

  3. $\dfrac34$

  4. $\dfrac35$

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Correct Option: A

For the special rule of multiplication of probability, the events must be

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

  1. Empirical

  2. Bayesian

  3. Independent

  4. none of these

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Correct Option: C

In a simultaneous throw of two dice, what is the probability of getting a total of 10 or 11 ?

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

  1. $\displaystyle \frac{7}{12}$

  2. $\displaystyle \frac{5}{36}$

  3. $\displaystyle \frac{1}{6}$

  4. $\displaystyle \frac{1}{4}$

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Correct Option: B
Explanation:
Let A denotes the event of getting a total of 10 and B denotes the event of getting a total of 11.
Total outcomes = $6\times 6 $
A= {(5,5),(6,4),(4,6)}
n(A) = $3$
$\therefore $ p(A) = $\dfrac {3}{36}  $
B={(6,5),(5,6)}
n(B) = 2
$\therefore $ p(B)= $\dfrac {2}{36}  $
$\therefore $ p(A or B) = p(A) + p(B) 
                   = $\dfrac {3}{36} + \dfrac {2}{36} $
                   = $\dfrac {5}{36} $
Option B is correct.

How many times must a man toss a fair coin, so that the probability of having at least one head is more than $80 \%?$

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

  1. $3$

  2. $>3$

  3. $<3$

  4. none of these

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Correct Option: B
Explanation:
In any fair coin toss, P (getting a head) = P (getting a tail) i.e., p=q=$\dfrac 12$
We need to find n such that the probability of getting at least one head is more than $80\%$
$P(X≥1)=1−P(X<1)>80\%$
$\implies 1−P(X=0)>\dfrac 8{10}\\\implies P(X=0)<1−\dfrac 8{10}\\\implies P(X=0)<\dfrac 2{10} or P(X=0)<\dfrac 15$
For a bionomial distribution, $P(X=0)=^nC _0\left(\dfrac 12\right)^0\left(\dfrac 12\right)^{n−0}=\left(\dfrac 12\right)^n$
$\implies \left(\dfrac 12\right)^n<\dfrac 1{5}\\\implies 2^n>5$
Since $2^1=2,2^2=4, 2^3=8,2^4=16$, the minimum value for n that satisfies the inequality is $n=3$, i.e, the coin should be tossed $3$ or more times.