Question

A pair of unbiased dice are rolled together till a sum of either 5 or 7 is obtained. The probability that 5 comes before 7 is

• A. 2/5
• B. 3/5
• C. 4/5
• D. None of these

Answer 1

Answer: (A)

2/5

Answer 2

Let A denote the event that a sum of 5 occurs, B the event that a sum of 7 occurs and C the event that neither a sum of 5 nor a sum of 7 occurs. We have

P(1) = $\frac { 26 } { 36 } = \frac { 13 } { 18 }$

Thus P(A occurs before B)

$= \frac { 1 } { 9 } + \left( \frac { 13 } { 18 } \right) \times \frac { 1 } { 9 } + \left( \frac { 13 } { 18 } \right) ^ { 2 } \frac { 1 } { 9 }$ +....... $= \frac { \frac { 1 } { 9 } } { 1 - \frac { 13 } { 18 } } = \frac { 2 } { 5 }$

[sum of an infinite G.P.]