Question

A small commuter plane has 30 seats. The probability that any particular passenger will not show up for a flight is 0.1, independent of other passengers. The airline sells 32 tickets for the flight. What is the probability that more passengers show upthan there are seats available?

Answer 1

The probability will be = 0.15641

Explanation:

We have given-

probability that any particular passenger will not show up for a flight = 0.1

probability that any particular passenger will show up for a flight = 0.9

the prob. that more passengers show up than, this will follow binomial distribution:

p = prob. of success = 0.9

1 - p = prob. of failure = 0.1

Pr( x = 31) + Pr(x = 32) =
`³²c₃₁ * (0.9)³¹ * (0.1)¹ + ³²c₃₂ * (0.9)³² * (0.1)⁰`

= 0.12208 + 0.03433

= 0.15641