7 Amir is trying to thread a needle. On each attempt the probability that he is successful is 0.3 , independently of any other attempt. The random variable \(X\) represents the number of attempts that he takes to thread the needle.
- Find \(\mathrm { P } ( X = 5 )\).
- During the course of a day, Amir has to thread 6 needles.
Determine the probability that it takes him more than 3 attempts to be successful for at least 4 of the 6 needles.
- Amaya is also trying to thread a needle. On each attempt the probability that she is successful is \(p\), independently of any other attempt. The probability that Amaya takes 2 attempts to thread a particular needle is \(\frac { 28 } { 121 }\).
Determine the possible values of \(p\).