3 A tennis player is practising her serve. Each time she serves, she has a \(55 \%\) chance of being successful (getting the serve in the required area without hitting the net). You should assume that whether she is successful on any serve is independent of whether she is successful on any other serve.
- Find the probability that the player is not successful in any of her first three serves.
- Determine the probability that the player is successful at least 10 times in her first 20 serves.
- Determine the probability that the player is successful for the first time on her fifth serve.
- Determine the probability that the player is successful for the fifth time on her tenth serve.
Another player is also practising his serve. Each time he serves, he has a probability \(p\) of being successful. You should assume that whether he is successful on any serve is independent of whether he is successful on any other serve.
The probability that he is successful for the first time on his second serve is 0.2496 and the probability that he is successful on both of his first two serves is less than 0.25 .
- Determine the value of \(p\).