Class 11 Mathematics Binomial Distribution MCQs Set 01

Question. The number of parameters of B.D. are
(a) 4
(b) 3
(c) 2
(d) 1
Answer: (c) 2

Question. If \( X \sim B(20, 1/2) \). The variance is
(a) 3
(b) 4
(c) 5
(d) 6
Answer: (c) 5

Question. Let X be a B(2, p) and Y be an independent B(4, p). If P(X ≥ 1) = 5/9, then P(Y ≥ 1) is
(a) \( \frac{61}{65} \)
(b) \( \frac{65}{81} \)
(c) \( \frac{1}{2} \)
(d) \( \frac{1}{3} \)
Answer: (b) \( \frac{65}{81} \)

Question. When a coin is tossed n times if the probability for getting 6 heads is equal to the probability for getting 8 heads then, the value of n is
(a) 8
(b) 10
(c) 12
(d) 14
Answer: (d) 14

Question. The least number of times a fair coin must be tossed so that the probability of getting atleast one head is atleast 0.8 is
(a) 1
(b) 2
(c) 3
(d) 4
Answer: (c) 3

Question. In a box containing 15 identical bulbs, 5 are defective. If 5 bulbs are drawn at random from the box with replacement, The probability that atleast one of them is defective is
(a) \( \frac{32}{343} \)
(b) \( \frac{211}{243} \)
(c) \( \frac{80}{243} \)
(d) \( \frac{32}{243} \)
Answer: (b) \( \frac{211}{243} \)

Question. When a coin is tossed, p(X = r heads) =
(a) \( \frac{^nC_r}{2^n} \)
(b) \( \frac{^nC_r}{2^{n-1}} \)
(c) \( \frac{^nC_n}{2^{n-1}} \)
(d) \( \frac{^nC_n}{2^n} \)
Answer: (a) \( \frac{^nC_r}{2^n} \)

Question. A binomial distribution has a mean of 5 and variance 4. The number of trials is
(a) 20
(b) 16
(c) 25
(d) 10
Answer: (c) 25

Question. If X is binomial variate with E(X) = 5 and variance 4. The parameters of the distribution are
(a) \( \frac{1}{4}, 20 \)
(b) \( \frac{1}{5}, 20 \)
(c) \( 25, \frac{1}{5} \)
(d) \( \frac{1}{25}, \frac{1}{5} \)
Answer: (c) \( 25, \frac{1}{5} \)

Question. If the mean of the binomial distribution is 25. Then standard deviation lies in the interval given below (Eamcet 1992)
(a) [0, 5)
(b) (0, 5]
(c) [0, 25)
(d) (0, 25]
Answer: (a) [0, 5)

Question. The standard deviation \( \sigma \) of \( (q + p)^{16} \) is 2. The mean of the distribution is
(a) 2
(b) 8
(c) 16
(d) 20
Answer: (b) 8

Question. In a binomial distribution, if AM = 4 and variance = 3. Then n is
(a) 10
(b) 12
(c) 4
(d) 3
Answer: (b) 12

Question. In a binomial distribution mean is 4.8 and variance is 2.88, then the parameter n is
(a) 8
(b) 12
(c) 16
(d) 20
Answer: (b) 12

Question. A fair coin is tossed 6 times. The variance of number of heads is
(a) 3
(b) 3/2
(c) 3/4
(d) 2
Answer: (b) 3/2

Question. In a binomial distribution mean = \( \frac{11}{4} \) and variance = \( \frac{15}{16} \), then the probability of success is
(a) \( \frac{1}{2} \)
(b) \( \frac{29}{44} \)
(c) \( \frac{1}{4} \)
(d) \( \frac{3}{4} \)
Answer: (b) \( \frac{29}{44} \)

Question. A machine manufacturing screws is known to produce 5% defectives. In a random sample of 15 screws the probability that there are exactly 3 defectives is
(a) \( \frac{16}{20} \)
(b) \( \frac{17}{20} \)
(c) \( ^{15}C_3 \left(\frac{1}{20}\right)^3 \left(\frac{19}{20}\right)^{12} \)
(d) \( \frac{18}{20} \)
Answer: (c) \( ^{15}C_3 \left(\frac{1}{20}\right)^3 \left(\frac{19}{20}\right)^{12} \)

Question. The probability of a man hitting the target is \( \frac{1}{4} \). If he fires 7 times the probability of his hitting the target atleast once is
(a) \( \left(\frac{3}{4}\right)^7 \)
(b) \( 1 - \left(\frac{3}{4}\right)^7 \)
(c) \( \left(\frac{1}{4}\right)^7 \)
(d) \( 1 - \left(\frac{1}{4}\right)^7 \)
Answer: (b) \( 1 - \left(\frac{3}{4}\right)^7 \)

Question. A box contains 3 red marbles and 2 white marbles. A marble is drawn and replaced three times from the box. The probability that exactly one red marble is drawn is
(a) 3/5
(b) 9/125
(c) 36/125
(d) 6/125
Answer: (c) 36/125

Question. Of the bolts produced by a factory 2% are defective. In a shipment of 3600 bolts from the factory, the expected number of defective bolts is
(a) 144
(b) 72
(c) 36
(d) 18
Answer: (b) 72

Question. If X is a binomial variate with n=6 and 9P(X=4)=P(X=2), the parameter p is
(a) 3/4
(b) 1/3
(c) 1/4
(d) 1/2
Answer: (c) 1/4

Question. Twenty identical coins each with probability p of showing heads are tossed. The probability of heads showing on 10 coins is same as that of heads showing on 11 coins then p =
(a) 1/2
(b) 10/21
(c) 11/21
(d) 13/21
Answer: (c) 11/21

Question. The probability that a student is not a swimmer is \( \frac{1}{5} \). Out of 5 students the probability that exactly four are swimmers is
(a) \( \left(\frac{4}{5}\right)^3 \)
(b) \( \left(\frac{1}{5}\right)^4 \)
(c) \( ^5C_4 \left(\frac{4}{5}\right)^4 \left(\frac{1}{5}\right) \)
(d) \( ^5C_4 \left(\frac{1}{5}\right)^4 \left(\frac{4}{5}\right) \)
Answer: (c) \( ^5C_4 \left(\frac{4}{5}\right)^4 \left(\frac{1}{5}\right) \)

Question. The probability that India wins a cricket test match against England is \( \frac{1}{3} \). If India and England play 3 matches, the probability that India will win atleast one match is
(a) 8/27
(b) 19/27
(c) 1/27
(d) 9/27
Answer: (b) 19/27

Question. In a binomial distribution, the probability of getting a success is \( \frac{1}{4} \) and the standard deviation is 3. Then its mean is
(a) 12
(b) 10
(c) 8
(d) 6
Answer: (a) 12

Question. The probability of obtaining 2 heads when an unbiased coin is tossed 5 times is
(a) 5/8
(b) 4/9
(c) 5/16
(d) 4/16
Answer: (c) 5/16

Question. Six unbiased coins are tossed, the probability of obtaining atleast two heads is
(a) 50/64
(b) 55/64
(c) 57/64
(d) 60/64
Answer: (c) 57/64

Question. The probability of answering 6 out of 10 questions correctly in a true or false examination is
(a) \( ^{10}C_4 \left(\frac{1}{2}\right)^4 \)
(b) \( ^{10}C_6 \left(\frac{1}{2}\right)^6 \)
(c) \( ^{10}C_6 \left(\frac{1}{2}\right)^{10} \)
(d) \( ^{10}C_6 \left(\frac{1}{2}\right)^8 \)
Answer: (c) \( ^{10}C_6 \left(\frac{1}{2}\right)^{10} \)

Question. On the average if it rains on 5 days in every 30 days, the probability that there will be rain on exactly three days of a given week is
(a) \( ^7C_3 \left(\frac{1}{6}\right)^3 \)
(b) \( ^7C_3 \left(\frac{5}{6}\right)^3 \)
(c) \( ^7C_3 \left(\frac{1}{6}\right)^3 \left(\frac{5}{6}\right)^4 \)
(d) \( ^7C_3 \left(\frac{1}{6}\right)^4 \)
Answer: (c) \( ^7C_3 \left(\frac{1}{6}\right)^3 \left(\frac{5}{6}\right)^4 \)

Question. A and B play a game in which A's chance of winning is \( \frac{1}{5} \). In a series of 6 games, the probability that A will win all the 6 games is
(a) \( ^6C_2 \left(\frac{1}{5}\right)^6 \)
(b) \( ^6C_6 \left(\frac{1}{5}\right)^6 \left(\frac{4}{5}\right)^0 \)
(c) \( \left(\frac{4}{5}\right)^6 \)
(d) \( ^6C_5 \left(\frac{1}{5}\right)^5 \)
Answer: (b) \( ^6C_6 \left(\frac{1}{5}\right)^6 \left(\frac{4}{5}\right)^0 \)

Question. The probability that in a family of 4 children there will be atleast one boy is
(a) 13/16
(b) 15/16
(c) 14/16
(d) 12/16
Answer: (b) 15/16

Question. A fair coin is tossed four times. The probability that tails exceed heads in number is
(a) 1/4
(b) 5/16
(c) 7/16
(d) 9/16
Answer: (b) 5/16

Question. A symmetrical die is thrown 6 times. If getting an odd number is a success, the probability of at the most 5 successes is
(a) 5/64
(b) 15/64
(c) 63/64
(d) 36/64
Answer: (c) 63/64

Question. Five cards are drawn successively with replacement from a well shuffled pack of 52 cards. The probability that all the five cards are spades
(a) \( ^5C_5 \left(\frac{1}{4}\right)^5 \)
(b) \( \frac{5}{52} \)
(c) \( \left(\frac{3}{4}\right)^5 \)
(d) \( \left(\frac{3}{4}\right)^2 \)
Answer: (a) \( ^5C_5 \left(\frac{1}{4}\right)^5 \)

Question. In six throws of a die, getting 4 or 5 is considered as a success. The mean number of successes is
(a) 4
(b) 3
(c) 2
(d) 1
Answer: (c) 2

Question. If A and B are two equally strong table tennis players, the probability that A beats B in exactly three games out of 4 games is
(a) 1/6
(b) 1/5
(c) 1/4
(d) 1/2
Answer: (c) 1/4

Question. A student is given 6 questions in a true or false examination. If he gets 4 or more correct answers, he passes the examination. The probability that he passes the examination is
(a) 5/32
(b) 7/32
(c) 11/32
(d) 3/32
Answer: (c) 11/32

Question. The incidence of occupational disease in an industry is such that the workers have a 20% chance of suffering from it. The probability that out of 6 workers chosen at random, not even one will suffer from that disease is
(a) \( \left(\frac{1}{5}\right)^6 \)
(b) \( \left(\frac{4}{5}\right)^6 \)
(c) \( \left(\frac{1}{5}\right)^0 \)
(d) \( \left(\frac{1}{5}\right)^3 \)
Answer: (b) \( \left(\frac{4}{5}\right)^6 \)

Question. The chance that a person with two dice, the faces of each being numbered 1 to 6, will throw aces exactly 4 times in 6 trials is
(a) \( \left(\frac{1}{36}\right)^4 \)
(b) \( \left(\frac{35}{36}\right)^4 \)
(c) \( ^6C_4 \left(\frac{1}{36}\right)^4 \left(\frac{35}{36}\right)^2 \)
(d) \( ^6C_4 \left(\frac{35}{36}\right)^4 \left(\frac{1}{36}\right)^2 \)
Answer: (c) \( ^6C_4 \left(\frac{1}{36}\right)^4 \left(\frac{35}{36}\right)^2 \)

Question. If 10% of the attacking air crafts are expected to be shot down before reaching the target, the probability that out of 5 aircrafts atleast four will be shot before they reach the target is
(a) \( 4 \left(\frac{1}{10}\right)^4 \)
(b) \( 5 \left(\frac{1}{10}\right)^4 \)
(c) \( (4.6) \left(\frac{1}{10}\right)^4 \)
(d) \( 6 \left(\frac{1}{10}\right)^4 \)
Answer: (c) \( (4.6) \left(\frac{1}{10}\right)^4 \)

Question. The probability of A winning a game is 2/3. In a series of 4 such games the probability that A will win more than half of the games is
(a) 32/81
(b) 33/81
(c) 16/27
(d) 8/27
Answer: (c) 16/27