Binomial Distribution

Binomial distributionBinomial distribution is a discrete distribution, and is used for situations where individual trials, experiments, or tests have only two possible outcomes such as success/failure, go/no-go, defectetive/non-defective or

pass/fail.

rNr pprNr

NpNr

)1(

)!(!

!),/(p

N is the sample size ( in a trial)

r is the number of events of interest observed in the sample (i.e. failures, or defectives)

p is the proportion of events of interest in the population

p(r / N, p) also can be written as

P (r, N, p) not to be confused with p.

Introduction

3

Fixed number of trials (n)

4

Introduction

5

Introduction

Third property : Trials are Independent

The Binomial Distribution The Formula for P(X=r)

?

Here, n=Number of trials r=Probability of success

Lets check about 10

Total 10 (Same)

Binomial Distribution - Examples

Now I look at using the formula in solving the following questions.

Q.(1)The manufacturer of a bag of sweets claims that there is a 90% chance that the bag contains some toffees. If 20 bags are chosen. What is the probability that

(i) all the bags contain toffees(ii) more than 18 bags contain toffees

Tree Diagram

Solution

Q.(2) In clinical trials a certain drug has an 8% success rate of curing a known disease. If 15 people are known to have the disease. What is the probability of at least 2 being cured.

Solution