probability of two dependent events: if two events, a and b, are dependent, then the probability of...
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Probability of Two Dependent Events: If two events, A and B, are dependent, then the probability of both events occurring is…
P(A and B) = P(A) * P(B following A)
13.4 Probabilityof Compound Events
Probability of Two Independent Events: If two events, A and B, are both independent, then the probability of both events occurring is…
P(A and B) = P(A)*P(B)
Example of Independent Events: What is the probability of rolling a 4 on a die 3 times in a row?
13.4 Probabilityof Compound Events
P(4) = P(three 4s) =
Roll 1 Roll 2 Roll 3
P(4) * P(4) * P(4)
=
≈ or 0.423%
Example of Dependent Events: What is the probability of drawing 6 hearts from a deck of cards without replacement?
13.4 Probabilityof Compound Events
P(six hearts) =
Draw 1 Draw 2 Draw 3
* * *
=
≈ or 0.008429%
Draw 4 Draw 5 Draw 6
* * 84 7
Example: Suppose the odds of the Sixers beating the Kings in Basketball was 5 : 2. What is the probability of the Sixers beating the Kings 4 times in a row?
13.4 Probabilityof Compound Events
Game 1 Game 2 Game 3
* * *
Odds = 𝑃 (𝑆𝑖𝑥𝑒𝑟𝑠𝑤𝑖𝑛)𝑃 (𝐾𝑖𝑛𝑔𝑠𝑤𝑖𝑛)
=
5727
Game 4
P(4 wins) =
P(Sixers win)
= = ≈
Example: A particular bag of marbles contains 4 red, 6 green, 2 blue, and 5 white marbles. What is the probability of picking a red, white, and blue marble, in that order?
What would the probability be with replacement?
13.4 Probabilityof Compound Events
P(r,w,b) =
Pick 1 Pick 2 Pick 3
* * P(r,w,b) = ≈ .0098
P(r,w,b) =
Pick 1 Pick 2 Pick 3
* * P(r,w,b) = ≈ .0081
13.4 Probability of MutuallyExclusive Events and Inclusive Events
Probability of Mutually Exclusive Events: If two events, A and B, are mutually exclusive, then the probability that either A OR B occurs is…
P(A or B) = P(A) + P(B)
Mutually Exclusive Events: If two events, A and B, are mutually exclusive, then that means that if A occurs, than B cannot, and vice versa.
Probability of Inclusive Events: If two events, A and B, are inclusive, then the probability that either A or B occurs is…
P(A or B) = P(A) + P(B) – P(A and B)
Inclusive Events: If two events, A and B, are inclusive, then that means that if A occurs, B could also occur, and vice versa.
13.4 Probability of MutuallyExclusive Events and Inclusive Events
Example: A particular bag of marbles contains 4 red, 6 green, 2 blue, and 5 white marbles. If 3 marbles are picked, what is the probability of picking all reds or all greens?
13.4 Probability of MutuallyExclusive Events and Inclusive Events
P(red or greens) = P(red) + P(green)
=
=
= = ≈
mutually exclusive event
¿𝐶(4,3 )
𝐶(17 , 3)
¿4
680+
20680
= = ≈
+𝐶(6,3 )
𝐶(17,3)
Example: Slips of paper numbered 1 to 15 are placed in a box. A slip of paper is drawn at random. What is the probability that the number picked is either a multiple of 5 or an odd number?
13.4 Probability of MutuallyExclusive Events and Inclusive Events
inclusive event
P(mult of 5 or odd) = P(mult of 5) + P(odd) – P(5 and odd)
=
= ≈ =
Example: Two cards are picked out of a standard deck. What is the probability of both cards being either face cards or clubs?
13.4 Probability of MutuallyExclusive Events and Inclusive Events
inclusive event
P(face or clubs)
= =
=
=
≈
= P(face) + P(club) – P(face and club)
+[1352
∗ 1251 ]−[ 3
52∗ 2
51 ]
Example: 4 coins are tossed. What is the probability of obtaining 2 heads or 1 tail?
13.4 Probability of MutuallyExclusive Events and Inclusive Events
P(2 heads or 1 tail )
=
= = =
mutually exclusive event
=
= P(2 heads) + P(1 tail)
In a particular group of hospital patients, the probability of having high blood pressure is , the probability of having arteriosclerosis is , and the probability of having both is
a) Determine whether the events are mutually exclusive or mutually inclusive.
b) What is the probability that a patient in this group has either high blood pressure or arteriosclerosis?
13.4 Probability of MutuallyExclusive Events and Inclusive Events
Probability of Two Independent Events: P(A and B) = P(A)*P(B)
Probability of Two Dependent Events:
P(A and B) = P(A) * P(B following A)
Probability of Mutually Exclusive Events: P(A or B) = P(A) + P(B)
Probability of Inclusive Events: P(A or B) = P(A) + P(B) – P(A and B)