English
Tamil Nadu Board of Secondary EducationHSC Commerce Class 12

An experiment succeeds twice as often as it fails, what is the probability that in next five trials there will be three successes - Business Mathematics and Statistics

Advertisements
Advertisements

Question

An experiment succeeds twice as often as it fails, what is the probability that in next five trials there will be three successes

Sum
Advertisements

Solution

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(three successes) = P(X = 3)

= `5"c"_3 (2/3)^2 (1/3)^(5 - 3)`

= `5"c"_2 (2/3)^3 (1/3)^2`   .....`["nc"_x = "nc"_("n"  x)]`

= `(5 xx 4)/(1 xx 2) xx 8/27 xx 1/9`

= `10 xx 8/243`

= `80/243`

shaalaa.com
Distribution
  Is there an error in this question or solution?
Chapter 7: Probability Distributions - Exercise 7.1 [Page 156]

APPEARS IN

Samacheer Kalvi Business Mathematics and Statistics [English] Class 12 TN Board
Chapter 7 Probability Distributions
Exercise 7.1 | Q 20. (i) | Page 156

RELATED QUESTIONS

In a particular university 40% of the students are having newspaper reading habit. Nine university students are selected to find their views on reading habit. Find the probability that all those selected have newspaper reading habit


Mention the properties of poisson distribution


The average number of phone calls per minute into the switchboard of a company between 10.00 am and 2.30 pm is 2.5. Find the probability that during one particular minute there will be no phone at all


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 at most 3 accidents


Define Standard normal variate


In a photographic process, the developing time of prints may be looked upon as a random variable having the normal distribution with a mean of 16.28 seconds and a standard deviation of 0.12 second. Find the probability that it will take less than 16.35 seconds to develop prints


Choose the correct alternative:

Forty percent of the passengers who fly on a certain route do not check in any luggage. The planes on this route seat 15 passengers. For a full flight, what is the mean of the number of passengers who do not check in any luggage?


Vehicles pass through a junction on a busy road at an average rate of 300 per hour. What is the expected number passing in two minutes?


The birth weight of babies is Normally distributed with mean 3,500g and standard deviation 500g. What is the probability that a baby is born that weighs less than 3,100g?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×