Question

Past records reveal that during a particular date, out of 9 vessels expected to arrive at the Mumbai harbour exactly 7 reached the harbour safely. If 3 vessels were expected to arrive there on a particular date, the probability that exactly two would arrive at the harbour safely, is:

• A. 91/243
• B. 92/243
• C. 95/243
• D. None

Answer 1

Answer: (D)

None

Answer 2

On the basis of past records, the probability of safe arrival of a vessel on Mumbai harbour, is 7/9. Since arrival of all the vessels is independent and there are only two possibilities on every vessel namely safe arrival and unsafe arrival, we can use the binomial distribution here, we have

n = 3, p = 7/9, q = 2/9 and r = 2.

using formula P(r) = ${ } ^ { n } C _ { r } p ^ { r } q ^ { n - r }$ , we have P(2)

= ${ } ^ { 3 } C _ { 2 } \left( \frac { 7 } { 9 } \right) ^ { 2 } \left( \frac { 2 } { 9 } \right) = \frac { 98 } { 243 }$ .