Probability Simple

1
Probability (Simple)
P(A) ( favorable outcomes of A)/( total
possible outcomes of A)
For example, consider a deck of 52 cards P (A
ace) 4/52 1/13 P(A
spade) 13/52 1/4
2
Example 1
Two fair six-sided dice are rolled what is the
probability of having 5 as the sum of the number?
Ans favourable outcomes (1,4),(4,1),(2,3)(3,
2) 4 total outcomes 66 36
P(A 5) 4/36 1/9
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Example 2
Two six-sided dice are rolled what is the
probability of having 12 as the sum of the
numbers?
Ans favorable outcomes (6,6) 1
total outcomes 36 P(A12) 1/36
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Probability (Compound)

• P(A and B) P(A) P(B)
• P(A or B) P(A) P(B) P(A and B)
• P( not A) 1 P(A)
• NOTE if A and B have nothing in common
• then P(A and B) 0

5
Example 1
If a fair coin is tossed twice, what is the
probability that on the first toss the coin lands
heads and on the second toss the coin lands
tails? (A)    1/6 (B)      1/3 (C)     1/4
(D)    1/2 (E)     1
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Example 2

• If a fair coin is tossed twice what is the
  probability that it will land either heads both
  times or tails both times?
• (A)      1/8
• (B)      1/6
• (C)     1/4
• (D)       1/2
• (E)     1

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Example 3
A bowman hits his target in 1/2 of his shots.
What is the probability of him missing the target
at least once in three shots?
Ans Total number outcomes 222 8
Total number not favorable 1 P(not A)
1/8 P(A) 1- P(A) 1- 1/8 7/8
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Example 4
What is the probability that a card selected from
a deck will be either an ace or a spade?
(A)      2/52 (B)      2/13 (C)       7/26
(D)      4/13 (E)      17/52
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Example 5

• If someone draws a card at random from a deck and
  then, without replacing the first card, draws a
  second card, what is the probability that both
  cards will be aces?

Ans P(A ace and B ace) P(Aace)P(Bace)

4/52 3/51
1/13 1/17
1/221
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Example 6
If there are 30 red and blue marbles in a jar,
and the ratio of red to blue marbles is 23, what
is the probability that, drawing twice, you will
select two red marbles if you return the marbles
after each draw?
Ans Red 2x , Blue 3x, 2x 3x
30, x 6, Red 12, Blue 18 P(A red
and B red) P(A red) P(B red)
12/30
12/30 2/5 2/5
4/25

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Example 7

• Now consider the same question as example 6 with
  the condition that you do not return the marbles
  after each draw.

Ans P(A red and B red) P(A red) P(B
red)
12/30 11/29 2/5 11/29
22/145