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Probability of Compound Events

Probability of Compound Events with Replacement

In the first video, we are going to work with probability of compound events.

Probability of Compound Events: The probability of multiple events happening

For rolling a dice and flipping a coin:
P(6) and P(Head)
The probability of rolling a dice is \frac{1}{6} and the probability of flipping a head is \frac{1}{2}

Multiplying the two probability together, since both events have to be happening, we now have
\frac{1}{6}\times\frac{1}{2}=\frac{1}{12}

Probability of Compound Events Without Replacement

In the second video, we are going to work with probability of compound events without replacement.

Without replacement, the total number of outcomes decreases after each drawing.

For example:
In a bag, there are 3 blue marbles, 2 red marbles, and 4 yellow marbles. What is the probability of drawing two blue marbles and one yellow marble without placing the marbles back into the bag?

Here, we would have
P(blue, blue, yellow)

Which is the same thing as
P(blue, blue, yellow)=\frac{3}{9}\times\frac{2}{8}\times\frac{4}{7}
after substitution

Reduce any term if necessary
P(blue, blue, yellow)=\frac{1}{3}\times\frac{1}{4}\times\frac{4}{7}
P(blue, blue, yellow)=\frac{1}{3}\times\frac{1}{1}\times\frac{1}{7}

Multiply across
P(blue, blue, yellow)=\frac{1}{21}

Therefore, the probability of drawing two blue marbles and a yellow marble without replacement would be \frac{1}{21}.