Question

write
explain how to determine the probability
of a compound event. be sure to include
both types of compound events.
remember
a compound event combines two or more
events using the word and or the word or.
practice

1. lucia is selecting colored tiles out of a bag to use for an art project.

the table shows the number of tiles of each color that are in the bag.
lucia selects one tile at random from the bag.
a. how many tiles are in her bag?
b. complete the probability model for selecting tiles from the bag.

outcome	blue	yellow	pink	green	purple
color	number of tiles
blue	10
yellow	12
pink	6
green	3
purple	9

c. what is the probability that lucia selects a green or
purple tile?
d. what is the probability that lucia selects a pink, green,
or purple tile?
e. what is the probability that lucia selects a pink and purple tile in
one draw?

Explanation:

Step1: Confirm total tile count

$10 + 12 + 6 + 3 + 9 = 40$

Step2: Solve part c: Add green/purple probabilities

$\frac{3}{40} + \frac{9}{40} = \frac{12}{40} = \frac{3}{10}$

Step3: Solve part d: Add pink/green/purple probabilities

$\frac{6}{40} + \frac{3}{40} + \frac{9}{40} = \frac{18}{40} = \frac{9}{20}$

Step4: Solve part e: Mutually exclusive event

A single draw cannot select two different tiles, so probability = $0$

To determine compound event probability:

1. For "or" (mutually exclusive events, no overlap): Add the probabilities of each individual event.
2. For "and" (simultaneous single draw): If events cannot happen at the same time, the probability is 0. If drawing with replacement, multiply the probabilities of each event.

Answer:

a. 40
b. Blue: $\frac{10}{40}$, Yellow: $\frac{12}{40}$, Pink: $\frac{6}{40}$, Green: $\frac{3}{40}$, Purple: $\frac{9}{40}$
c. $\frac{3}{10}$
d. $\frac{9}{20}$
e. $0$

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