In this lesson, we’re going to do the following using a table that shows the test results of 200 students who took a GED test.

  • Calculate the probability of independent events and show the relationship between independent events and their probabilities
  • Calculate the probability of dependent events and show the relationship between dependent events and their probabilities
  • Explain the difference between independent events and dependent events

Let’s start with the probability of independent events. Look at the table below.

Contingency table of independent events

To let consist be the case that a randomly selected student passed the test

To let male be the case that a randomly selected student is male.

Calculate these two probabilities: P (pass) and P (pass / male)

P (pass) =

120
/
200

= 0.60

P (passport / male) =

66
/
110

= 0.60

We notice that P (pass) = P (pass / male)

This means that the probability of passing is equal to the probability of passing if the student is male.

In other words, it doesn’t matter if the student is male, the success rate is still the same.

Existence does not depend on gender.

From this we can conclude that the two events “pass” and “male” are independent events. No event will affect the other.

In general, two events A and B are independent if the occurrence of one does not affect the likelihood of the other occurring.

P (A) = P (A / B) or P (B) = P (B / A)

Since passing does not depend on gender, if we calculate P (pass) and P (pass / female) you should also get 0.60.

In fact, P (pass / female) =

66
/
110

In fact, P (pass / female) =

54
/
90

= 0.60 = P (passed)

What about the result shown in the table in the lesson on marginal probability?

Contingency table of dependent events

P (pass) =

114
/
200

= 0.57

P (passport / male) =

46
/
102

= 0.45

Note that adding the “male” event changed the probability.

Since the event “male” changes the probability, the two events “pass” and “male” are dependent events.

Likewise, the two events “pass” and “female” are dependent events.

Notice below what P (pass / female) equals!

P (pass / female) =

68
/
98

= 0.69

Since 0.69 is greater than 0.45, women are more likely to pass the test than men.

For this result, the pass here depends on the gender.

In general, two events, A and B, are dependent if the occurrence of one affects the likelihood of occurrence of the other.

P (A) ≠ P (A / B) or P (B) ≠ P (B / A)




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