Help! Finding the Probability of Multiple Events

Here's the good news about GED style probability problems: they really aren't as hard as they look!
This example, from the experienced level practice of the Crash Course Probability lesson, is like that, much simpler than you'd think. Thanks to Shu Ma Nyie who posted this one in our Facebook Group, Free GED Prep from Light & Salt Learning.

[@user-cp9fv7lu2o]

A die is tossed so that the chance is a 1 is x/4 the chance of throwing a 2 is 1/4, and the chance of throwing a 6 is 1-x/4. The chance of throwing a 3, a 4 or a 5 is 1/6. The die is thrown twice. Prove that of the provabilityof throwing a total of 7 is (x-x²)/8+5/36. Find the maximum chance of this event.

[@LightandSaltLearning]

This is above the level of the GED. What test are you preparing for?

[@shumanyie5532]

Thank you Kate for explaining. I didn't got my answer right because i multiply it by 5/6 and 6/6 for four times.

[@LightandSaltLearning]

Does it make sense now?

[@shumanyie5532]

@@LightandSaltLearning yes it does!

[@surekhayamini5031]

That helped me🎉🎉🎉🎉🎉🎉🎉🎉

[@LightandSaltLearning]

Wonderful! I'm so glad it helped!