Prize value Number of prizes £1 million 2 6 11 24 60 116 £100,000 £50,000 £25,000 £10,000 £5,000 £1,000 £500 £100 £50 £25 1,973 5.919 32,061 32,061 3,358,678
Premium bonds are an investment issued by the UK Government. A single bond costs £1. The bond holder is eligible to win a prize in a lottery held monthly, in which each bond has an equal chance of being drawn. (For the purposes of this question, ignore the requirement that the bond has to be held for 3 months before it is included in the monthly lottery.) A typical list of monthly prizes is shown in the table below. The chance of winning a prize (of any value) with a single bond is currently about 1 in 34,500. The maximum permissible bond holding is 50,000 bonds.
(a) Consider a bond holder with the maximum holding of 50,000 bonds. What is the
(b) Consider a bond holder with 1000 bonds. What is the probability of winning more than 2 prizes (of any value) in total over 5 years (60 monthly draws)?
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