- A biased 4 -sided spinner has the numbers \(6,7,8\) and 10 on it.
The discrete random variable \(X\) represents the score when the spinner is spun once and has the following probability distribution,
| \(x\) | 6 | 7 | 8 | 10 |
| \(\mathrm { P } ( X = x )\) | 0.5 | 0.2 | \(q\) | \(q\) |
where \(q\) is a probability.
- Find the value of \(q\)
Karen spins the spinner repeatedly until she either gets a 7 or she has taken 4 spins.
- Show that the probability that Karen stops after taking her 3rd spin is 0.128
The random variable \(S\) represents the number of spins Karen takes.
- Find the probability distribution for \(S\)
The random variable \(N\) represents the number of times Karen gets a 7
- Find \(\mathrm { P } ( S > N )\)