'Shall' should only be used with the first person singular and plural. 'Are going to' and 'will' are both fine.

My guess is that this is a typo and that the options should are A are going to B shall C will The best answer, as you correctly say, Sasha, is 'will'. 'are going to' is not the best answer because, as Morgan explains, this form usually indicates something pre-planned, so it isn't a prediction. That said, it is still possible. You can say 'I predict that .... is going to happen' in the sense that it seems inevitable. 'shall' is wrong. 'Shall' is only used with the second person ('you') when the speaker is being particularly insistent that something is the case, and is making a point of contradicting something previously said or believed. My favourite example of 'You shall....' is in the fairy tale Cinderella, when the fairy godmother waves her magic wand and exclaims 'You SHALL

A and C are the same, but "going to" in this sense means that the future has already been planned out. Therefore, it wouldn't be a prediction. B is the correct answer, as "shall" means that the future is not certain to them. It's the same as "will," which is why "will" wasn't an answer. "I predict that you SHALL marry someone rich and famous." Hope this helped! ^^

"Shall" is often used in place of "will"; it's fairly formal/old fashioned, but it still sees use sometimes.

..... OOPS. I pressed 'return' instead of caps lock. So to continue about 'shall'....The fairy godmother says to Cinderella 'You SHALL go to the ball' . Cinderella didn't believe she'd get to go to the ball, and the godmother is emphatically correcting her. She's being insistent, and contradicting what had previously been said or believed. In your example phrase above there is no contradiction, or previous suggestion that the person wasn't going to marry someone rich and famous, so I'm afraid that you can't use 'shall'.