The number of free gifts that Jan receives in a week is denoted by \(X\). Name a suitable probability distribution with which to model \(X\), giving the value(s) of any parameter(s). State any assumption(s) necessary for the distribution to be a valid model.
Assume now that your model is valid.
Find
(a) \(\mathrm { P } ( X \leqslant 2 )\),
(b) \(\mathrm { P } ( X = 2 )\).
Find the probability that, in the next 7 weeks, there are exactly 3 weeks in which Jan receives exactly 2 free gifts.
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The diagram shows 7 cards, each with a digit printed on it. The digits form a 7 -digit number.
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