probability independent & dependent events. definitions: events are independent events if the...
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P R O B A B I L I T Y
INDEPENDENT & DEPENDENT EVENTS
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DEFINITIONS:
• Events are independent events if the occurrence of one event does not affect the probability of the other. • Events are dependent events if the occurrence
of one does affect the probability of the other.
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DETERMINE IF THE EVENTS ARE DEPENDENT OR INDEPENDENT.
1. Getting tails on a coin toss and rolling a 6 on a number cube.
1. Tossing a coin does not affect rolling a number cube, so the two events are independent.
2. Getting 2 red gumballs out of a gumball machine.
1. After getting one red gumball out of a gumball machine, the chances for getting the second red gumball have changed, so the two events are dependent.
3. Rolling a 6 two times in a row with the same number cube.
1. The first roll of the number cube does not affect the second roll, so the events are independent.
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Three separate boxes each have one blue marble and one green marble. One marble is chosen from each box. What is the probability of choosing a blue marble from each box?
P(blue, blue, blue) =12
· 12
· 12
= 18
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FIND EACH PROBABILITY IF YOU SPIN BOTH SPINNERS.
1. P (white, A)
2. P (striped, A)
3. P (not striped, B)
4. P (not white, B)
P = 1/5(1/3) =
1/15
P = 2/5(1/3) =
2/15
P = 3/5(2/3) =
6/15 =
P = 4/5(2/3) =
8/15
2/5
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To calculate the probability of two dependent events occurring, do the following:
1. Calculate the probability of the first event.
2. Calculate the probability that the second event would occur if the first event had already occurred.
3. Multiply the probabilities.
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FIND EACH PROBABILITY IF YOU PICK A CARD, DO NOT REPLACE IT, THE PICK A SECOND CARD.
1. P(black, then white)
2. P(black, then black)
3. P(white, then white)
P = 5/8 * 3/7 =
15/56
P = 5/8 * 4/7 =
5/14
1
2
P = 3/8 * 2/7 =
3/28
1
4
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IF THE LETTERS TO THE WORD DEPENDENT ARE PLACED IN A BOX…
If two letters are chosen at random, what is the probability that both letters are vowels?
P(vowel, vowel) = 3/9 * 2/8 = 1/3 * 1/4 = 1/12