binomial experiments

Defi

nitio

nBinomial Experiment:

Defi

nitio

nBinomial Experiment:

►experiment is repeated for fixed number of trials

Defi

nitio

nBinomial Experiment:

►experiment is repeated for fixed number of trials

► two possible outcomes:

Defi

nitio

nBinomial Experiment:

►experiment is repeated for fixed number of trials

► two possible outcomes:

► Success or Failure

Defi

nitio

nBinomial Experiment:

►experiment is repeated for fixed number of trials

► two possible outcomes:

► Success or Failure

► probability of success is constant

Defi

nitio

nBinomial Experiment:

►experiment is repeated for fixed number of trials

► two possible outcomes:

► Success or Failure

► probability of success is constant

► x counts the number of successful

trials

Notation

Symbol

Description

n the number of times a trial is repeated

Notation

Symbol

Description

n the number of times a trial is repeated

p the probability of success

Notation

Symbol

Description

n the number of times a trial is repeated

p the probability of success

q the probability of failure

Notation

Symbol

Description

n the number of times a trial is repeated

p the probability of success

q the probability of failure

x the number of successes out of n trials

Exam

ple

You roll a pair of 6-sided dice 5 times, and note whether or not you rolled a pair of doubles like(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)

Exam

ple

You roll a pair of 6-sided dice 5 times, and note whether or not you rolled a pair of doubles like (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)

► n =5 (you rolled the dice 5 times)► A binomial experiment has a fixed

number of trials

Exam

ple

You roll a pair of 6-sided dice 5 times, and note whether or not you rolled a pair of doubles like (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)

► n =5 (you rolled the dice 5 times)► A binomial experiment has a fixed

number of trials

Exam

ple

You roll a pair of 6-sided dice 5 times, and note whether or not you rolled a pair of doubles like (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)

► n =5 (you rolled the dice 5 times)► A binomial experiment has a fixed

number of trials

Exam

ple

You roll a pair of 6-sided dice 5 times, and note whether or not you rolled a pair of doubles like (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)

► n =5 (you rolled the dice 5 times)► A binomial experiment has a fixed

number of trials

Exam

ple

You roll a pair of 6-sided dice 5 times, and note whether or not you rolled a pair of doubles like (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)

► n =5 (you rolled the dice 5 times)► A binomial experiment has a fixed

number of trials

Exam

ple

You roll a pair of 6-sided dice 5 times, and note whether or not you rolled a pair of doubles like (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)

► n =5 (you rolled the dice 5 times)► A binomial experiment has a fixed

number of trials► p = 6/36, the probability of success

► A binomial experiment has a fixed rate of success

Exam

ple

You roll a pair of 6-sided dice 5 times, and note whether or not you rolled a pair of doubles like (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)

► n =5 (you rolled the dice 5 times)► A binomial experiment has a fixed

number of trials► p = 6/36, the probability of success

► A binomial experiment has a fixed rate of success

► q = 30/36, the probability of failure► q = 1-p

Exam

ple

You roll a pair of 6-sided dice 5 times, and note whether or not you rolled a pair of doubles like (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)

► n =5 (you rolled the dice 5 times)► A binomial experiment has a fixed

number of trials► p = 6/36, the probability of success

► A binomial experiment has a fixed rate of success

► q = 30/36, the probability of failure► q = 1-p

► x = {0, 1, 2, 3, 4, 5}, the number of successes out of n trials

Revi

ewBinomial experiments:

Revi

ewBinomial experiments:

• fixed number of trials, n

Revi

ewBinomial experiments:

• fixed number of trials, n

• Probability of success, p, is the same for all trials

Revi

ewBinomial experiments:

• fixed number of trials, n

• Probability of success, p, is the same for all trials

• probability of failure, q, is the compliment of p (q = 1 – p).

Revi

ewBinomial experiments:

• fixed number of trials, n

• Probability of success, p, is the same for all trials

• probability of failure, q, is the compliment of p (q = 1 – p).

• x is the number of successes out of n trials, x = 0, 1, 2, 3, …, n