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Probability of independent events

We can calculate the probabilities of two or more independent events by multiplying each probability.

Independent events are not affected by each over. For example, probability of A and B equals to the product of probability A and probability B:

$$P(A \ \text{and} \ B) = P(A) × P(B)$$

Solved examples

Let's do some examples to see how it works.

Example No. 1

You flip three quartes. What is the probability that you flip three heads?

Solution: P(A and B and C) = P(A) * P(B) * P(C) = 1/2 * 1/2 * 1/2 = 1/8

Example No. 2

At the same time you toss a coin and roll a dice. What is the probability of getting a coin head and even number of dice?

The chance to get head is 1/2 and the chance to get even number of dice is also 1/2, because needed numbers are 2, 4, 6 and total number of outcomes is 6, so 3/6 = 1/2.
Now we can get the probability: P(A and B) = 1/2 * 1/2 = 1/4

2019-03-03