Four teachers dress to feel warm. Teacher A has a hat and a scarf and gloves, B has only a hat, C only a scarf and D has only gloves. One teacher out of the four is selected at random.

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Four teachers dress to feel warm. Teacher A has a hat and a scarf and gloves, B has only a hat, C only a scarf and D has only gloves. One teacher out of the four is selected at random. Show that though each pair of events H = 'the teacher selected has a hat', S = 'the teacher selected has a scarf', and G = 'the teacher selected has gloves' are independent, all three of these events are not independent.