A die is thrown twice. What is the probability that
(i) 5 will not come up either time?
(ii) 5 will come up at least once?
[Hint : Throwing a die twice and throwing two dice simultaneously are treated as the same experiment]
📚 Submitted Answer
Solution:
Total number of possible outcomes when a die is thrown twice:
Each die has 6 faces numbered from 1 to 6. When a die is thrown twice, the total number of possible outcomes is:
6 × 6 = 36
(i) Probability that 5 will not come up either time:
Number of outcomes where 5 comes up at least once:
To find the number of outcomes where 5 comes up at least once, we can list all such favorable outcomes:
- First die shows 5: (5,1), (5,2), (5,3), (5,4), (5,5), (5,6)
- Second die shows 5: (1,5), (2,5), (3,5), (4,5), (6,5)
Total favorable outcomes where 5 comes up at least once = 11
Number of outcomes where 5 does not come up either time:
36 – 11 = 25
Probability that 5 will not come up either time:
Number of favorable outcomes / Total number of outcomes = 25/36
(ii) Probability that 5 will come up at least once:
This is the complement of the event in part (i).
Probability = 1 − Probability that 5 does not come up either time = 1 − 25 / 36 = 11 /36
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