Bernoulli’s trials:
Bernoulli Experiment with n Trials Here are the rules for a Bernoulli
experiment.
1. The experiment is repeated a fixed number of times (n times).
2. Each trial has only two possible outcomes, “success” and
“failure”. The possible outcomes are exactly the same for each
trial.
3. The probability of success remains the same for each trial. We
use p for the probability of success (on each trial) and q = 1 − p
for the probability of failure.
4. The trials are independent (the outcome of previous trials has
no influence on the outcome of the next trial).
5. We are interested in the random variable X where X = the
number of successes. Note the possible values of X are 0, 1, 2,
3, . . . , n. An experiment in which a single action, such as flipping
a coin, is repeated identically over and over. The possible results of
n = number of trials
k = number of successes
n – k = number of failures
p = probability of success in one trial
q = 1 – p = probability of failure in one trial
Problem 1: If the probability of a bulb being defective is 0.8,
then what is the probability of the bulb not being defective.
Solution: Probability of bulb being defective,
p = 0.8 Probability of bulb not being defective,
q = 1 - p = 1 - 0.8 = 0.2
Problem 2: 10 coins are tossed simultaneously where the
probability of getting head for each coin is 0.6. Find the
probability of getting 4 heads.
Solution: Probability of getting head, p = 0.6
Probability of not getting head, q = 1 - p = 1 - 0.6 = 0.4
Probability of getting 4 heads out of 10,
