# Former pro football star O.J. Simpson was accused of murdering his wife. In the trial, a defense attorney pointed out that although Simpson had been guilty of earlier spousal abuse, annually only about 40 women are murdered by their partner per 100,000 incidents of partner abuse. But this was misleading. Every year it is estimated that about 5 of every 100,000 women in the US who suffer partner abuse are killed by someone other than their partner. Draw a tree diagram for women who suffer partner abuse. Calculate the following (round to 5 decimal places):a) What is the probability that a woman who suffers partner abuse will be murdered by their partner?b) What is the probability that a woman who suffers partner abuse will be murdered (by anyone)?c) What is the probability that a murdered woman who suffered partner abuse was murdered by their partner?

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Former pro football star O.J. Simpson was accused of murdering his wife. In the trial, a defense attorney pointed out that although Simpson had been guilty of earlier spousal abuse, annually only about 40 women are murdered by their partner per 100,000 incidents of partner abuse. But this was misleading. Every year it is estimated that about 5 of every 100,000 women in the US who suffer partner abuse are killed by someone other than their partner. Draw a tree diagram for women who suffer partner abuse. Calculate the following (round to 5 decimal places):
a) What is the probability that a woman who suffers partner abuse will be murdered by their partner?
b) What is the probability that a woman who suffers partner abuse will be murdered (by anyone)?
c) What is the probability that a murdered woman who suffered partner abuse was murdered by their partner?

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Step 1

The tree diagram is given as follows:

Step 2

a).

From the above tree diagram,

The number of women who suffers partner abuse is 100,000.

Number of women who suffers partner abuse will be murdered by their partner is 40.

Therefore, probability that a woman who suffers partner abuse will be murdered by their partner is calculated as follows:

Step 3

b).

Number of women who suffers partner abuse will be murdered by anyone is 45.

Therefore, probability that a woman who suffers partner abuse will be murdered by anyone is calculated as follows:

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