A pair of dice is thrown. if it is known that one dice shows a 4, what is the probability that the other shows a 5?
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3
the probability is 3÷4 or 0.75 of getting 5 , if in one die 4 will appear.
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6
The probability that the other shows a 5 is 2/11.
- When two dices are thrown the samples obtained is
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)
- If one dice shows a 4, the the sample is left with
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6) (1,4) (2,4) (3,4) (5,4) (6,4)
Total = 11 samples
- Now the samples where the other shows a 5 is
(4,5) and (5,4)
number of events = 2
- Therefore, probability is
Probability = Number of events / Total samples
Probability = 2/11
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