- In an experiment a group of children each repeatedly throw a dart at a target. For each child, the random variable \(H\) represents the number of times the dart hits the target in the first 10 throws.
Peta models \(H\) as \(\mathrm { B } ( 10,0.1 )\)
- State two assumptions Peta needs to make to use her model.
- Using Peta's model, find \(\mathrm { P } ( H \geqslant 4 )\)
For each child the random variable \(F\) represents the number of the throw on which the dart first hits the target.
Using Peta's assumptions about this experiment,
- find \(\mathrm { P } ( F = 5 )\)
Thomas assumes that in this experiment no child will need more than 10 throws for the dart to hit the target for the first time. He models \(\mathrm { P } ( F = n )\) as
$$\mathrm { P } ( F = n ) = 0.01 + ( n - 1 ) \times \alpha$$
where \(\alpha\) is a constant.
- Find the value of \(\alpha\)
- Using Thomas' model, find \(\mathrm { P } ( F = 5 )\)
- Explain how Peta's and Thomas' models differ in describing the probability that a dart hits the target in this experiment.