Advertisements
Advertisements
प्रश्न
An experiment succeeds twice as often as it fails, what is the probability that in next five trials there will be at least three successes
Advertisements
उत्तर
Success = 2 × fails
p = 2q
⇒ p = 2(1 – p)
p = 2 – 2p
⇒ p + 2p = 2
3p = 2 and p = `2/3`
q = 1 – p = `1 – 2/3`
q = `1/3` and n = 5
The binomial destribution is
P(X = x) = nCxpxqn-x
= `5"C"(2/3)^x (1/3)`
P(atleast three success)
= P(X ≥ 3)
= P(X = 3) + P(X = 4) + P(X = 5)
= `80/243 + 5"c"_4 (2/3)^4 + (1/3)^(5 - 4) + 5"c"_5 (2/5)^5 (1/3)^(5 - 5)`
= `80/243 + 5"C"_1 (16/81)(1/3) + 5"c"_0 (32/243)(1/3)^0`
= `80/243 + 80/243 + 32/243`
= `(80 + 80 + 32)/243`
= `192/243`
APPEARS IN
संबंधित प्रश्न
Derive the mean and variance of binomial distribution
The mean of a binomial distribution is 5 and standard deviation is 2. Determine the distribution
The distribution of the number of road accidents per day in a city is poisson with mean 4. Find the number of days out of 100 days when there will be no accident
The distribution of the number of road accidents per day in a city is poisson with mean 4. Find the number of days out of 100 days when there will be atleast 2 accidents
If the heights of 500 students are normally distributed with mean 68.0 inches and standard deviation 3.0 inches, how many students have height between 65 and 71 inches
Choose the correct alternative:
In turning out certain toys in a manufacturing company, the average number of defectives is 1%. The probability that the sample of 100 toys there will be 3 defectives is
Choose the correct alternative:
The random variable X is normally distributed with a mean of 70 and a standard deviation of 10. What is the probability that X is between 72 and 84?
Choose the correct alternative:
The starting annual salaries of newly qualified chartered accountants (CA’s) in South Africa follow a normal distribution with a mean of ₹ 180,000 and a standard deviation of ₹ 10,000. What is the probability that a randomly selected newly qualified CA will earn between ₹ 165,000 and ₹ 175,000?
The time taken to assemble a car in a certain plant is a random variable having a normal distribution of 20 hours and a standard deviation of 2 hours. What is the probability that a car can be assembled at this plant in a period of time. Between 20 and 22 hours?
X is a normally distributed variable with mean µ = 30 and standard deviation σ = 4. Find P(X > 21)
