fill in the blankIndependent and Mutually Exclusive Events 3.2 Independent and Mutually Exclusive Events1. Two events are independent if2. So, two events A and B are independent if one of the following identities is trueformula (2.1)formula (2.2)Note that the formula (2.2) can be derived from formula (1.1) and formula (2.1).3. If two events are NOT independent, then we say that they are dependent.4. The concept of independent events explains why P({HH}) = P({HT}) = P({TH}) = P({TT})1/4 for the experiment of tossing two fair coins. Challenge yourself to explain it!5. with replacement and without replacement• When an experiment for a probability is to select some members (or a sample) from a set,there are two ways to conduct the experiment: selecting members one by one with replacementand selecting them without replacement. These are different experiments. So, they may resultin different probabilities for the same event.• Do TRY IT 3.6 (with replacement)• What if you conduct the experiment of TRY IT 3.6 without replacement? Challenge yourselfto find the probability of getting at least one black card when the experiment is done withoutreplacement.6. Mutually Exclusive Events• A and B are mutually exclusive events if• When A and B are mutually exclusive, P(A And B) :• A simplest example. For the experiment of tossing a fair coin, the two events {H} and {T} aremutually exclusive.• If it is not known whether A and B are mutually exclusive, assume they are not until you canshow otherwise.Do all examples in the textbook.

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MATLAB: An Introduction with Applications

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Concept explainers

Compound Probability

Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.

Tree diagram

Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described.

Conditional Probability

By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.

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