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# Binomial Conditions

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### Over-booking

### Statistics - Maths of Real Life

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Age 16 to 18

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What does it mean for two trials to be *independent*? Make sure you are absolutely clear on this before you start!

Can you come up with examples where the trials are dependent? What do we mean by the probability of success of the second trial if it is dependent on the first trial?

You might find it helpful to think in terms of tree diagrams or two-way tables (if there are only two trials).

Bear in mind that if each trial is a repeat of the first trial with the same starting conditions, then it is likely to have the same probability of success and be independent of the first trial. So to find an example where these conditions are*not* met, the trials cannot possibly all look identical.

There are some example situations that might give you some ideas in Binomial or Not?

Can you come up with examples where the trials are dependent? What do we mean by the probability of success of the second trial if it is dependent on the first trial?

You might find it helpful to think in terms of tree diagrams or two-way tables (if there are only two trials).

Bear in mind that if each trial is a repeat of the first trial with the same starting conditions, then it is likely to have the same probability of success and be independent of the first trial. So to find an example where these conditions are

There are some example situations that might give you some ideas in Binomial or Not?

The probability that a passenger books a flight and does not turn up is 0.05. For an aeroplane with 400 seats how many tickets can be sold so that only 1% of flights are over-booked?

This pilot collection of resources is designed to introduce key statistical ideas and help students to deepen their understanding.