Translate -2x+7>17 on a number line
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By the binomial theorem we know that
The probability that exactly 5 of 8 support the incumbent is the term
So at least five of eight support is the sum of this term and beyond,
No particularly easy way of calculating that except popping it into Wolfram Alpha which reports
Shouldn't half the terms work out to .6 ? Interestingly it's not exactly .6 but pretty close at .594.