3. The homework diaries and completed homework of two Students A and B, are examined.

There is a probability of 0.4 that Student A does not make a note in her diary homework set. She always does the homework if it is written in her diary, but never does the homework if it is not written in.

There is a probability of 0.8 that Student B writes the homework given

in her diary. When she does this, she will do the homework 90% of the time. If she has nothing written in her diary then she checks with a friend,

who knows what the homework is 50% of the time; Student B always does the homework if she is told what it is by her friend.

C) If one piece of homework was given to a student but wasn’t done, find the probability that it was given to Student A.

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