Probability - Waiting-Time and Stopping-Rule Probabilities

Probability - Waiting-Time and Stopping-Rule Probabilities

A bag contains \(10\) orange-flavoured, \(14\) strawberry-flavoured, and \(16\) cherry-flavoured sweets which are of identical shapes and sizes. Benny selects a sweet at random from the bag. If it is not cherry-flavoured he replaces it and selects another sweet at random. He repeats the process until he obtains a cherry-flavoured sweet.

Calculate the probability that

  1. the first sweet selected is strawberry-flavoured and the fourth sweet is orange-flavoured,
  2. he selects an even number of sweets.

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Answer:(i) \(\frac{63}{2000}\) (ii) \(\frac38\)

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