Advertisements
Advertisements
प्रश्न
उत्तर
The repeated guessing of correct answers from multiple-choice questions is Bernoulli trials. Let X represent the number of correct answers by guessing in the set of 5 multiple-choice questions.
Probability of getting a correct answer is, p `= 1/3`
` ∴ "q" = 1 - "p" = 1 - 1/3 = 2/3`
Clearly, X has a binomial distribution with n = 5 and p `= 1/3`
∴ p (X = x) = `""^"n""C"_"x" "q"^("n"-"x")"p"^"x"`
` = ""^5"C"_"x" (2/3)^(5-"x").(1/3)^"x"`
P (guessing more than 4 correct answers) = P(X ≥ 4)
= P (X = 4)+ (X = 5)
` = ""^5"C"_4(2/3).(1/3)^4 + ""^5"C"_5(1/3)^5`
` = 5. 2/3 . 1/81 + 1 . 1/243`
` = 10/243 + 1/243`
` = 11/243`
APPEARS IN
संबंधित प्रश्न
A bag consists of 10 balls each marked with one of the digits 0 to 9. If four balls are drawn successively with replacement from the bag, what is the probability that none is marked with the digit 0?
In an examination, 20 questions of true-false type are asked. Suppose a student tosses a fair coin to determine his answer to each question. If the coin falls heads, he answers ‘true’; if it falls tails, he answers ‘false’. Find the probability that he answers at least 12 questions correctly.
A fair coin is tossed 9 times. Find the probability that it shows head exactly 5 times.
The probability that a bulb produced by a factory will fuse after 150 days of use is 0.05. Find the probability that out of 5 such bulbs none will fuse after 150 days of use
A man wins a rupee for head and loses a rupee for tail when a coin is tossed. Suppose that he tosses once and quits if he wins but tries once more if he loses on the first toss. Find the probability distribution of the number of rupees the man wins.
Suppose that a radio tube inserted into a certain type of set has probability 0.2 of functioning more than 500 hours. If we test 4 tubes at random what is the probability that exactly three of these tubes function for more than 500 hours?
The probability that a student entering a university will graduate is 0.4. Find the probability that out of 3 students of the university none will graduate
The probability that a student entering a university will graduate is 0.4. Find the probability that out of 3 students of the university only one will graduate .
Suppose X has a binomial distribution with n = 6 and \[p = \frac{1}{2} .\] Show that X = 3 is the most likely outcome.
The probability of a shooter hitting a target is \[\frac{3}{4} .\] How many minimum number of times must he/she fire so that the probability of hitting the target at least once is more than 0.99?
Find the probability that in 10 throws of a fair die, a score which is a multiple of 3 will be obtained in at least 8 of the throws.
Determine the binomial distribution whose mean is 20 and variance 16.
A dice is thrown thrice. A success is 1 or 6 in a throw. Find the mean and variance of the number of successes.
The mean and variance of a binomial distribution are \[\frac{4}{3}\] and \[\frac{8}{9}\] respectively. Find P (X ≥ 1).
A die is thrown three times. Let X be 'the number of twos seen'. Find the expectation of X.
The mean of a binomial distribution is 10 and its standard deviation is 2; write the value of q.
If in a binomial distribution n = 4 and P (X = 0) = \[\frac{16}{81}\] , find q.
A rifleman is firing at a distant target and has only 10% chance of hitting it. The least number of rounds he must fire in order to have more than 50% chance of hitting it at least once is
A fair die is thrown twenty times. The probability that on the tenth throw the fourth six appears is
A fair coin is tossed 99 times. If X is the number of times head appears, then P (X = r) is maximum when r is
The least number of times a fair coin must be tossed so that the probability of getting at least one head is at least 0.8, is
A biased coin with probability p, 0 < p < 1, of heads is tossed until a head appears for the first time. If the probability that the number of tosses required is even is 2/5, then p equals
A five-digit number is written down at random. The probability that the number is divisible by 5, and no two consecutive digits are identical, is
If the mean and variance of a binomial distribution are 4 and 3, respectively, the probability of getting exactly six successes in this distribution is
The probability that a bulb produced by a factory will fuse after 150 days of use is 0.05. Find the probability that out of 5 such bulbs more than one will fuse after 150 days of use
Find the mean and variance of the random variable X which denotes the number of doublets in four throws of a pair of dice.
If X follows binomial distribution with parameters n = 5, p and P(X = 2) = 9, P(X = 3), then p = ______.
If a fair coin is tossed 10 times. Find the probability of getting at most six heads.
In three throws with a pair of dice find the chance of throwing doublets at least twice.
