Why is 2-tail p-value twice the 1-tail p-value?

Why is the two-tail p-value always twice the one-tail p-value in a t-test?

In the t-test output below, notice that the two-tail p-value is 0.66852 while the one-tail p-value is 0.33426. The two-tail p-value is twice the one-tail p-value. Why is this true?

t-test output

The two-tail p-value is defined as P > |t|.  That is, the two-tail p-value is P > absolute value of t.

The t statistic is -0.433, thus P > |-0.433| which can be written P(>0.433) + P(<-0.433). Because the t-distribution is symmetrical about the mean, these two probabilities are equal.

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