A) \[2/5\]
B) \[3/5\]
C) \[4/5\]
D) \[\frac{1}{5}\]
Correct Answer: A
Solution :
[a]| Consider the events |
| A = Sum of 5 occurs |
| B = Sum of 7 occurs |
| C = Neither sum of 5 nor sum of 7 occurs |
| \[P(A)=\frac{1}{9},P(B)=\frac{1}{6},P(C)=\frac{13}{18}\] |
| P (A occurs before B) \[=P(A\,\text{or}\,(C\cap A)\,\text{or}\,(C\cap C\cap A)\,\text{or}...)\] |
| \[=P\,(A)+P(CA)+P(CCA)+...\] |
| \[=\frac{1}{9}+\frac{13}{18}\times \frac{1}{9}+{{\left( \frac{13}{18} \right)}^{2}}\times \frac{1}{9}+...\] |
| \[=\frac{1}{9}\left( 1+\frac{13}{18}+{{\left( \frac{13}{18} \right)}^{2}}+... \right)\] |
| \[=\frac{1}{9}\left( \frac{1}{1-\left( \frac{13}{18} \right)} \right)=\frac{2}{5}\] |
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