# 1028 defendants in criminal court cases were interviewed. It was found that 72 pled not-guilty. Of those 72, 14 were not sent to prison. Additionally, 392 of the defendants were sent to prison. a....

1028 defendants in criminal court cases were interviewed. It was found that 72

pled not-guilty. Of those 72, 14 were not sent to prison. Additionally, 392 of the

defendants were sent to prison.

a. What is the probability that a defendant either pled guilty or was sent to

prison?

b. What is the probability that a defendant either pled not-guilty or was not sent

to prison?

c. What is the probability that a defendant pled guilty and was sent to prison?

d. What is the probability that a defendant was not sent to prison given they pled

guilty?

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a. 956 assumed guilty pleas didn't go to prison. That should be 956, plus the 58 "not guilty" pleas that went to prison (the 956 includes the 392 who went to prison) which would give us 1,014 out of 1,028 probability or `1014/1028~~.986`

b. We know that of 72 not guilty pleas, 14 were not sent to prison. We also know that only 450 of all the defendants did go to prison. That means that 578 (1,028-450) did not go to prison. We add to that the 58 who pled "not guilty" but did go to prison and we get 636 out of 1,028 pled not guilty or did not go to prison. `636/1028~~.619`

c. Answering this question requires the assumption that none of the defendants pled "no contest." On that assumption we are told that 392 defendants went to prison and the language indicates that they were not amongst the 72 who pled "not guilty." So if we assume that everyone who wasn't amongst the 72 pled guilty and we are told 392 of them went to prison, the probability is 392 out of 1,028 that a defendant pled guilty and was sent to prison. `392/1028~~.381`

d. Again we have to assume that none of the defendants pled "no contest." Only 72 pled "not guilty" and the assumption is that everyone who didn't plead "not guilty" pled "guilty" and that's 1,028-72= 956. So we assume 956 guilty pleas. Of these 956, we are told that 392 went to prison. 956-392= 564. 564 of the 1,028 defendants did not go to prison even though they pled guilty. The probability is 564 out of 1,028 or `564/1028~~.549`