Advertisements
Advertisements
प्रश्न
A die is thrown 6 times. If ‘getting an odd number’ is a success, find the probability of at most 5 successes.
Advertisements
उत्तर
Let X = number of successes, i.e. number of odd numbers.
p = probability of getting an odd number in a single throw of a die
∴ p = `3/6 = 1/2` and q = `1 - "p" = 1 - 1/2 = 1/2`
Given: n = 6
∴ X ∼ B`(6, 1/2)`
The p.m.f. of X is given by
`p("X = x") = "^nC_x p^x q^(n - x)`
i.e. p(x) = `"^6C_x (1/2)^x (1/2)^(6 - x)`
` = "^6C_x (1/2)^6,` x = 0, 1, 2, ...,6
P(at most 5 successes) = P[X ≤ 5]
= 1 - P [X > 5]
= 1 - p(6) = `1 - "^6C_6 (1/2)^6`
`= 1 - 1 xx 1/64 = 63/64`
Hence, the probability of at most 5 successes is `63/64`.
APPEARS IN
संबंधित प्रश्न
The probability that a certain kind of component will survive a check test is 0.6. Find the probability that exactly two of the next four components tested will survive.
A die is thrown 6 times. If ‘getting an odd number’ is a success, find the probability of 5 successes.
A pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability of two successes.
Five cards are drawn successively with replacement from a well-shuffled deck of 52 cards; find the probability that all the five cards are spades.
In a box of floppy discs, it is known that 95% will work. A sample of three of the discs is selected at random. Find the probability that none of the floppy disc work.
In a box of floppy discs, it is known that 95% will work. A sample of three of the discs is selected at random. Find the probability that exactly one floppy disc work.
In a box of floppy discs, it is known that 95% will work. A sample of three of the discs is selected at random. Find the probability that exactly two floppy disc work.
Choose the correct option from the given alternatives:
The mean and the variance of a binomial distribution are 4 and 2 respectively. Then the probability of 2 successes is
Choose the correct option from the given alternatives:
For a binomial distribution, n = 5. If P(X = 4) = P(X = 3), then p = ______
For a binomial distribution, n = 4. If 2P(X = 3) = 3P(X = 2), then p = ______.
If X ~ B(4, p) and P(X = 0) = `16/81`, then P(X = 4) = ______.
Let X ~ B(10, 0.2). Find P(X = 1).
Let X ~ B(10, 0.2). Find P(X ≤ 8).
The probability that a mountain-bike travelling along a certain track will have a tyre burst is 0.05. Find the probability that among 17 riders: exactly one has a burst tyre
The probability that a mountain-bike travelling along a certain track will have a tyre burst is 0.05. Find the probability that among 17 riders: two or more have burst tyre.
The probability that a lamp in a classroom will be burnt out is 0.3. Six such lamps are fitted in the class-room. If it is known that the classroom is unusable if the number of lamps burning in it is less than four, find the probability that the classroom cannot be used on a random occasion.
A large chain retailer purchases a certain kind of electronic device from a manufacturer. The manufacturer indicates that the defective rate of the device is 3%. The inspector of the retailer picks 20 items from a shipment. What is the probability that the store will receive at most one defective item?
The probability that a machine will produce all bolts in a production run within specification is 0.998. A sample of 8 machines is taken at random. Calculate the probability that all 8 machines.
The probability that a machine will produce all bolts in a production run within specification is 0.998. A sample of 8 machines is taken at random. Calculate the probability that at most 6 machines will produce all bolts within specification.
The probability that a machine develops a fault within the first 3 years of use is 0.003. If 40 machines are selected at random, calculate the probability that 38 or more will not develop any faults within the first 3 years of use.
A computer installation has 10 terminals. Independently, the probability that any one terminal will require attention during a week is 0.1. Find the probabilities that 0.
A computer installation has 10 terminals. Independently, the probability that any one terminal will require attention during a week is 0.1. Find the probabilities that 2.
A computer installation has 10 terminals. Independently, the probability that any one terminal will require attention during a week is 0.1. Find the probabilities that 3 or more, terminals will require attention during the next week.
In a large school, 80% of the pupil like Mathematics. A visitor to the school asks each of 4 pupils, chosen at random, whether they like Mathematics.
Calculate the probabilities of obtaining an answer yes from 0, 1, 2, 3, 4 of the pupils.
In a large school, 80% of the pupil like Mathematics. A visitor to the school asks each of 4 pupils, chosen at random, whether they like Mathematics.
Find the probability that the visitor obtains answer yes from at least 2 pupils:
- when the number of pupils questioned remains at 4.
- when the number of pupils questioned is increased to 8.
It is observed that it rains on 12 days out of 30 days. Find the probability that it rains exactly 3 days of week.
It is observed that it rains on 12 days out of 30 days. Find the probability that it it will rain at least 2 days of a given week.
If E(x) > Var(x) then X follows _______.
In a Binomial distribution with n = 4, if 2P(X = 3) = 3P(X = 2), then value of p is ______.
Choose the correct alternative:
A sequence of dichotomous experiments is called a sequence of Bernoulli trials if it satisfies ______
In Binomial distribution, probability of success ______ from trial to trial
If the sum of the mean and the variance of a binomial distribution for 5 trials Is 1.8, then p = ______.
If X follows a binomial distribution with parameters n = 10 and p. If 4P(X = 6) = P(X = 4), then p = ______
In a binomial distribution `B(n, p = 1/4)`, if the probability of at least one success is greater than or equal to `9/10`, then n is greater than ______.
In a binomial distribution `B(n, p = 1/4)`, if the probability of at least one success is greater than or equal to `9/10`, then n is greater than ______.
In a binomial distribution, n = 4 and 2P(X = 3) = 3P(X = 2), then q = ______.
A pair of dice is thrown 3 times. If getting a doublet is considered a success, find the probability of getting at least two success.
Solution:
A pair of dice is thrown 3 times.
∴ n = 3
Let x = number of success (doublets)
p = probability of success (doublets)
∴ p = `square`, q = `square`
∴ x ∼ B (n, p)
P(x) = nCxpx qn–x
Probability of getting at least two success means x ≥ 2.
∴ P(x ≥ 2) = P(x = 2) + P(x = 3)
= `square` + `square`
= `2/27`
If X is a binomial variable with range {0, 1, 2, 3, 4} and P(X = 3) = 3P(X = 4) then the parameter ‘p’ of the binomial distribution is
