Suppose That a Defendant Faces Charges of First-Degree Murder and of Third-Degree

Suppose that a defendant faces charges of first-degree murder and of third-degree murder. She has been offered a plea-bargained agreement under which she would serve five years in jail by pleading guilty to the third-degree charge. If she does not plead guilty, however, the case will go to a jury trial, and the jury will reach one of three verdicts: not guilty, guilty of third-degree murder, or guilty of first-degree murder. If the jury finds her not guilty, she will serve no time in jail; if the jury finds her guilty of third-degree murder, she will serve seven years in jail; if the jury finds her guilty of first-degree murder, she will serve forty years in jail. Suppose that her attorney believes that the probability is .3 that a jury would find her innocent and .6 that a jury would find her guilty of third-degree murder.
-By making the decision that you reached in part $b$ , does the defendant guarantee she will be better off than if she had made the other decision? Explain.