Question

Describe what it means when two events are independent? What would make two events dependent? How does it change the calculation of probability of each?

Answer 1

Answer)

When two events are independent then probability of first event doesn't affects the probability of other.

For example,

We have conducted a survey whether someone likes vanilla or strawberry icecream.

Out of 1000 people surveyed

400 said they like vanilla and 500 said, they like strawberry

Here we have two events

Event 1 : when a randomly chosen guy likes vannila.

Event 2 : when a randomly chosen guy likes strawberry.

Here, probability of event 1 = 400/1000 = 0.4

Probability of event 2 = 500/1000 = 0.5

Now here, whether the first chosen guy likes vannila or not, probability that the second guy would like vanilla would be same as 0.4, given that we are doing this with replacement.

Or second example can be of coin toss, no matter how many times you toss, probability that the another toss would result in tails will always be = 1/2 = 0.5

And when the two events are dependent, then the probability of one affects the probability of other

Lets take the previous example of the survey of 1000 individuals

But in this case we will do without replacement

So probability that the first chosen person likes vannila is = 0.4

And the probability that the second chosen person likes vannila will be 399/999 = 0.3993993993993

As we are not replacing the first one, so we are left with 399 persons who like vannila and 999 total individuals.

So, in this case we have dependent events.