During the college vacations, each day Ahmed either eats rice with probability 0.6, or eats bread with probability 0.4. Ahmed does not eat both on the same day. If he eats rice then the probability that he gains weight is 0.05. If he eats bread the probability that he gains weight is 0.75. (i) Find the probability that Ahmed gains weight on any particular day. (ii) Given that Ahmed gains weight on a particular day, find the probability that he is eating bread. (iii) There are 45 days of school holidays. Show that the variance of the number of days Ahmed eats bread is the same as the variance of the number of days that Ahmed eats rice.
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