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Independent Events Solutions

When one event does not affect the probability of another event, the events are independent .
 The Multiplication Rule for Independent Probability states: When A and B are independent events, then $P (A and B) = P (A) \cdot P (B)$ . 
The intersection symbol, ⋂, is sometimes used in place of the word “and.”

Note

Independent events can occur at the same time (simultaneously) or one after the other (consecutively).

When completing two events in a row, the phrase “with replacement” often represents independent probability because the total number of outcomes remains the same . 
When the occurrence of the first event changes the probability of subsequent events, the events are dependent . This topic will be taught in the next lesson.

State whether the scenarios represent independent or dependent events.

One card is selected from a deck, placed to the side, and another card is drawn.

Dependent

Independent

Independent

Determine the probability of rolling an eight-sided die and spinning the spinner arrow.

$P (7 \cap R) = \frac{1}{8} \cdot \frac{1}{4} = \frac{1}{32}$

even: {2, 4, 6, 8}, primary color: {red, blue, yellow}

$= \frac{4}{8} \cdot \frac{3}{4} = \frac{3}{8}$

$= \frac{7}{8} \cdot \frac{1}{4} = \frac{7}{32}$

$= \frac{2}{8} \cdot \frac{2}{4} = \frac{4}{32} = \frac{1}{8}$

What is the percent chance of flipping a coin and getting tails 3 times in a row?

$P (T, T, T) = {(\frac{1}{2})}^{3} = \frac{1}{8} = 0.125 = 1.25 %$