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CBSE Questions for Class 12 Commerce Applied Mathematics Standard Probability Distributions Quiz 7 - MCQExams.com

An experiment succeeds twice as often as it fails. Find the chance that in the next six trials, there shall be at least four successes.
  • 233729
  • 64729
  • 496729
  • 432729
8 coins are tossed simultaneously. The probability of getting at least 6 heads is
  • 57/64
  • 229/256
  • 7/64
  • 37/256
The probability that a marksman will hit a target is given as 1/Then his probability at least one hit in 10 shots is.
  • 1(45)10
  • 15
  • 115,
  • none of these.
A fair coin is tossed n times. if the probability that head occurs 6 times is equal to the probability that head occurs 8 times, then value of n is
  • 24
  • 48
  • 14
  • 16
If X and Y are independent binomial variate B(5,1/2) and B(7,1/2), then P(X+Y=3) is
  • 55/1024
  • 55/4098
  • 55/2048
  • None of these
A random variable X follows binomial distribution with mean a and variance b. Then
  • a>b>0
  • ab>1
  • a2ab is an integer
  • a2a+b is an integer
In a hurdle race, a runner has probability p of jumping over a specific hurdle. Given that in 5 trials, the runner succeeded 3 times, the conditional probability that the runner had succeeded in the first trail is 
  • 35
  • 25
  • 15
  • 45
A fair die is tossed eight times. Probability that on the eighth throw a third six is observed is
  • 8C35868
  • 7C25568
  • 7C25567
  • None of these
Suppose X B(n,p) and P(X=3)=P(X=5). If p>12, then
  • n7
  • n>8
  • n9
  • none of these
15 coins are tossed, then the probability of getting 10 heads will be
  • 51132768
  • 100132768
  • 300332768
  • 300532768
A bag contains three tickets numbered 1, 2 and 3. A ticket is drawn at random and put back in the bag, and this is done four times. The probability that the sum of the numbers drawn is even is
  • \dfrac {40}{81}
  • \dfrac {41}{81}
  • \dfrac {14}{27}
  • \dfrac {13}{81}
If X follows a binomial distribution with parameters n=100 and p=1/3, find r for which P(X=r) is maximum
  • 33
  • 22
  • 11
  • 15
The probability that X=3 equals
  • \displaystyle \frac {25}{216}
  • \displaystyle \frac {25}{36}
  • \displaystyle \frac {5}{36}
  • \displaystyle \frac {125}{216}
The probability that a marksman will hit a target is given as \displaystyle \frac{1}{5} ,then his probability of at least one hit in 10 shots is 
  • \displaystyle 1-\left ( \frac{4}{5} \right )^{10}
  • \displaystyle \frac{1}{5^{10}}
  • \displaystyle 1-\frac{1}{5^{10}}
  • None of these
If the mean of a binomial distribution is 25, then find the interval in which the standard deviation lies.
  • [0,5)
  • (0,5]
  • [0,25)
  • (0,25]
Find the probability of getting 4 exactly thrice in 7 throws of a die
  • ^7C_3\left (\dfrac {1}{6}\right )^3\left (\dfrac {5}{6}\right )^4
  • ^7C_4\left (\dfrac {1}{6}\right )^4\left (\dfrac {5}{6}\right )^3
  • ^7C_4\left (\dfrac {1}{6}\right )^3\left (\dfrac {5}{6}\right )^4
  • ^7C_3\left (\dfrac {1}{6}\right )^4\left (\dfrac {5}{6}\right )^3
Numbers are selected at random, one at a time, from the two digit numbers 00, 01, 02,....., 99 with replacement. An event E occurs if & only if the product of the two digits of a selected number is 18. If four numbers are selected, find the probability that the event E occurs at least 3 times.
  • \dfrac{97}{25^4}
  • \dfrac{1}{25^4}
  • \dfrac{95}{25^4}
  • \dfrac{90}{25^4}
Suppose X follows a binomial distribution with parameters n and p, where 0<p<1. If \displaystyle \frac { P\left( X=r \right)  }{ P\left( X=n-r \right)  } is independent of n and r, then
  • \displaystyle p=\frac { 1 }{ 2 }
  • \displaystyle p=\frac { 1 }{ 3 }
  • \displaystyle p=\frac { 1 }{ 4 }
  • None of these
If n distinct objects are distributed randomly into n distinct boxed
  • then the probability that no box is empty is \displaystyle \frac{n!}{n^{n}}
  • then the probability that exactly one box is empty is \displaystyle \frac{n!^{n}C_{2}}{n^{n}}
  • then the probability that a particular box get exactly r objects is \displaystyle \frac{^{n}C_{r}(n-1)^{n-r}}{n^{n}}
  • None of these
Anand plays with Karpov 3 games of chess. The probability that he wins a game is 0.5, looses with probability 0.3 and ties with probability 0.2. If he plays 3 games then find the probability that he wins atleast two games
  • 1/2
  • 1/3
  • 1/4
  • 1/5
A fair die is rolled (2n+1) times. The probability that the faces with even number show odd number of times is
  • \displaystyle \frac {3n+1}{4n+2}
  • \displaystyle \frac {3}{4}
  • \displaystyle \frac {2}{3}
  • \displaystyle \frac {1}{2}
The value of P(2) in a Binomial distribution when \displaystyle P=\frac{1}{6} and n = 5 is 
  • \displaystyle \dfrac{3125}{7776}
  • \displaystyle \dfrac{250}{7776}
  • \displaystyle \dfrac{1250}{7776}
  • \displaystyle \dfrac{25}{7776}
A fair coin is tossed at a fixed number of times. If the probability of getting exactly 3 heads equals the probability of getting exactly 5 heads, then the probability of getting exactly one head is 
  • \dfrac{1}{64}
  • \dfrac{1}{32}
  • \dfrac{1}{16}
  • \dfrac{1}{8}
The mean number of heads in three tosses of a coin is 
  • \displaystyle \frac{5}{2}
  • \displaystyle \frac{1}{2}
  • \displaystyle \frac{3}{2}
  • \displaystyle \frac{1}{8}
Given \displaystyle X\sim N\left( 10,36 \right)   what is the variance of X?
  • 10
  • \displaystyle \sqrt { 10 }
  • 36
  • 6
What is the possibility of getting at least 6 heads if eight coins are tossed simultaneously?
  • \dfrac{37}{256}
  • \dfrac{25}{57}
  • \dfrac{1}{13}
  • \dfrac{5}{27}
The probability that an event does not happen in one trial is 0.8. The probability that the event happens atmost once in three trials is
  • 0.896
  • 0.791
  • 0.642
  • 0.592
Suppose X follows a binomial distribution with parameters n and p, where 0 < p <1   ,\dfrac {P(X = r)}{P(X = n - r)} is independent of n for every r, then p =
  • \dfrac {1}{2}
  • \dfrac {1}{3}
  • \dfrac {1}{4}
  • \dfrac {1}{8}
Given \displaystyle X\sim B\left( n,p \right) 
If \displaystyle E\left( X \right) =6,var\left( X \right) =4.2 then what is the number of trials?
  • 21
  • 10
  • 20
  • 7
If X is a poisson variate such that \alpha =P(X = 1) = P (X = 2) then P (X = 4) =
  • 2\alpha
  • \dfrac {\alpha}{3}
  • \alpha e^{-2}
  • \alpha e^{2}
Two persons A and B are throwing an unbiased six faced die alternatively, with the condition that the person who throws 3 first wins the game. If A starts the game, the probabilities of A and B to win the same are respectively
  • \dfrac {6}{11}, \dfrac {5}{11}
  • \dfrac {5}{11}, \dfrac {6}{11}
  • \dfrac {8}{11}, \dfrac {3}{11}
  • \dfrac {3}{11}, \dfrac {8}{11}
If x follows the Binomial distribution with parameters n=6 and  p and 9P(X=4) = P(X=2), then p is 
  • \dfrac {1}{4}
  • \dfrac {1}{3}
  • \dfrac {1}{2}
  • \dfrac {2}{3}
The probability that an individual suffers a bad reaction from an in injection is 0.001. The probability that out of 2000 individuals exactly three will suffer bad reaction is 
  • \dfrac{2}{e^2}
  • \dfrac{2}{5e^2}
  • \dfrac{8}{5e^2}
  • \dfrac{4}{3e^3}
The number of times a fair coin must be tossed so that the probability of getting at least one head is 0.8 is-
  • 7
  • 6
  • 5
  • 3
A die is thrown a fixed number of times. If probability of getting even number 3 times is same as the probability of getting even number 4 times, then probability of getting even number exactly once is
  • \dfrac{1}{4}
  • \dfrac{3}{128}
  • \dfrac{5}{64}
  • \dfrac{7}{128}
A fair coin is tossed 99 times. Let X be the number of times heads occurs. Then P(X=r) is maximum when r is
  • 49
  • 52
  • 51
  • None of these
Out of 800 families with 4 children each, the expected percentage of families having almost 2 girls, is:
  • 68.75 \%
  • 69.25 \%
  • 62.50 \%
  • None of these
For a poisson distribution with parameter \lambda = 0.25, the value of the 2^{nd} moment about the origin is
  • 0.25
  • 0.3125
  • 0.0625
  • 0.025
If the mean and standard deviation of a binomial distribution are 12 and 2 respectively, then the value of its parameter p is
  • \cfrac{1}{2}
  • \cfrac{1}{3}
  • \cfrac{2}{3}
  • \cfrac{1}{4}
The mean and the variance in a binomial distribution are found to be 2 and 1 respectively. The probability P(X = 0) is
  • \dfrac{1}{2}
  • \dfrac{1}{4}
  • \dfrac{1}{8}
  • \dfrac{1}{16}
In a Poisson distribution if P\left( X=2 \right) =P\left( X=3 \right) then the value of its parameter \lambda is
  • 6
  • 2
  • 3
  • 0
If X is a Poisson's variate such that P(X=1)=3P(X=2), then find the variance of X.
  • \cfrac 38
  • \cfrac 13
  • \cfrac 23
  • \cfrac 54
If mean and variance of a Binomial variable X are 2 and 1 respectively, then the probability that X takes a value greater than 1 is
  • \dfrac{2}{3}
  • \dfrac{4}{5}
  • \dfrac{7}{8}
  • \dfrac{11}{16}
If the mean and variance of a binomial distribution are 4 and 2, respectively. Then, the probability of atleast 7 successes is
  • \dfrac {3}{214}
  • \dfrac {4}{173}
  • \dfrac {9}{256}
  • \dfrac {7}{231}
A box contains 15 green and 10 yellow balls. If 10 balls are randomly drawn, one-by-one, with replacement, then the variance of the number of green balls drawn is
  • \displaystyle\frac{12}{5}
  • 6
  • 4
  • \displaystyle\frac{6}{25}
Which of the following are correct regarding normal distribution curve?
(i) Symmetrical about the line X=\mu (Mean)
(ii) Mean = Median = Mode
(iii) Unimodal
(iv) Points of inflexion are at X=\mu \pm \sigma
  • (i), (ii)
  • (ii), (iv)
  • (i), (ii), (iii)
  • All of these
The probability that a student get success in a competition is \dfrac { 3 }{ 4 }. The probability that exactly 2 out of 4 students get success, is
  • \dfrac { 9 }{ 41 }
  • \dfrac { 25 }{ 128 }
  • \dfrac { 1 }{ 5 }
  • \dfrac { 27 }{ 128 }
The mode of the binomial distribution for which mean and standard deviation are 10 and \sqrt { 5 } respectively, is
  • 7
  • 8
  • 9
  • 10
If r.v. X\sim B\left( n=5,P=\cfrac { 1 }{ 3 }  \right), then P(2< X< 4)=...........
  • \cfrac { 80 }{ 243 }
  • \cfrac { 40 }{ 243 }
  • \cfrac { 40 }{ 343 }
  • \cfrac { 80 }{ 343 }
The probability that an event does not happen in one trial is 0.8.The probability that the event happens atmost once in three trails is 
  • 0.896
  • 0.791
  • 0.642
  • 0.592
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Practice Class 12 Commerce Applied Mathematics Quiz Questions and Answers