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Binomial Distribution
Characteristics of a Binomial Experiment (or called Bernoulli Experiment)
If the random variable X is the number of “successes” in n Bernoulli trials with each
trial having probability p of “success” and probability q of “failure” then
The expectation of the number of successes in a binomial distribution of n Bernoulli trials
with probability p of success on each trial is ________________.
Example 1
Determine a probability function(model) for the number of heads when tossing a fair coin five
times. Determine the expected number of heads using the formula and the definition of
expected. Verify that the sum of the probabilities equals 1.
Let X rep the random variable that represent the number of heads
Example 2
A test consists of 10 multiple choice questions each with 5 possible answers, of which only
one is correct. If the result of each question is chosen by random guessing, what is the
probability that 6 of the answers chosen will be correct?
Example 3
A bag contains 10 red marbles and 20 black marbles. A marble is chosen at random from the
bag. Its colour is noted and then it is returned to the bag. This process is repeated 5 times.
Find the probability of:
a) selecting a red marble exactly 3 of the 5 times
b) selecting a black marble 4 or more times
Example 4
In a computer chip factory, 35 out of every 1000 chips produced are defective. A batch of
20 chips is chosen at random.
a)What is the probability that at most 10% of the chosen chips are defective?
b) Determine the expected number of defective chips