7 In a game,players attempt to score a goal by kicking a ball into a net.The probability that Leno scores a goal is 0.4 on any attempt,independently of all other attempts.The random variable \(X\) denotes the number of attempts that it takes Leno to score a goal.
- Find \(\mathrm { P } ( X = 5 )\) .
............................................................................................................................................ - Find \(\mathrm { P } ( 3 \leqslant X \leqslant 7 )\) .
- Find the probability that Leno scores his second goal on or before his 5th attempt.
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Leno has 75 attempts to score a goal. - Use a suitable approximation to find the probability that Leno scores more than 28 goals but fewer than 35 goals.
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