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The probability of getting heads at least once is the same as saying the probability of getting heads: exactly once, exactly twice or exactly three times. This is also 1 minus the probability of getting ...

n(n+5)+2(n+3) = n²+5n+2n+6 = n²+7n +6 = (n+6)(n+1) = (n+6) x (n+1).
The difference between (n+6) and (n+1) is 5, so this is a product of two numbers with a difference of 5.

4x² + 6x - 4 > 0 2(2x² + 3x - 2) > 0 2(2x - 1)(x + 2) > 0
2x-1 = 0 --> 2x = 1 --> x = 0.5x+2 = 0 --> x = -2
x = 0.5

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There are 30 counters in total in the bag. If we visualise the ratio as there being x red counters and 5x green counters, we find that there are 6x counters in total in the bag, and thus we can conclude t...