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100 people are randomly positioned in a circle. 10 of the people are sick and not wearing masks. Of the other 90 people, 50 are

100 people are randomly positioned in a circle. 10 of the people are sick and not wearing masks. Of the other 90 people, 50 are wearing a mask and 40 are not. We say a person is isolated if the person to their left and right is wearing a mask.

a) What is the expected number of sick people who are not isolated?

b) For person i, let Xi be the indicator random variable of whether that person is isolated. If person i and j are not adjacent, is Xi independent from Xj?

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