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Probability and Odds Explained

The document discusses odds and probabilities. It defines odds in favor of an event as the ratio of the number of ways the event can occur to the number of ways it cannot occur. Odds against an event are defined as the ratio of the number of ways it cannot occur to the number it can occur. It then gives an example problem involving 3 shooters, A, B, and C, hitting a target. The odds are given as 1:2 in favor of A hitting, 1:2 in favor of B, and 2:3 against C hitting. It then calculates the individual probabilities of each shooter hitting the target and the probabilities of different combinations of shooters hitting or missing the target.

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Anu Amruth
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77 views2 pages

Probability and Odds Explained

The document discusses odds and probabilities. It defines odds in favor of an event as the ratio of the number of ways the event can occur to the number of ways it cannot occur. Odds against an event are defined as the ratio of the number of ways it cannot occur to the number it can occur. It then gives an example problem involving 3 shooters, A, B, and C, hitting a target. The odds are given as 1:2 in favor of A hitting, 1:2 in favor of B, and 2:3 against C hitting. It then calculates the individual probabilities of each shooter hitting the target and the probabilities of different combinations of shooters hitting or missing the target.

Uploaded by

Anu Amruth
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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QA Odds

Odds in favour of An Event and Odds Against An Event


In m be the number of ways in which an event occurs and n be the number of ways in which
it does not occur, then
(i)

odds in favour of the event =

(ii)

odds against the event =

(or m : n)

(or n : m)

Solved Examples:
1) 3 shooters A, B, C are hitting a target. Odds are 1 : 2 in favour of A, 1 : 2 in favour of
B & 2 : 3 against C hitting the target.
Answer:
Odds are 1 : 2 in favour of A

Odds are 1 : 1 in favour of B

Odds are 2 : 3 against C

P A 1

3
2
P ' A
3
P B 1

2
P ' B 1
2
PC 3

5
2
P' C
5

a) Find the probability that all three will hit the target.
1/3 x x 3/5 =
1
10

b) No one will hit the target.


2/3 x x 2/5 =
2

15

c) The target will be hit.


1 - 2/15
13

15

d) Find the probability that exactly 2 will be hit. A and B but not C= 1/3 x x 2/5 = 1/15
A and C but not B= 1/3 x x 3/5= 1/10
B and C but not A = 2/3 x x 3/5 = 1/5
Exactly two = 1/15 + 1/10 + 1/5 = 11 30

Proprietary and Confidential

ABS Classes

QA Odds

Proprietary and Confidential

ABS Classes

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