The Internal Revenue Service compiles data on income tax returns and summarizes its findings in Statistics of Income. The first two columns of Table 5.21 show a frequency distribution (number of returns) for adjusted gross income (AGI) from federal individual income tax returns, where K = thousand.

A federal individual income tax return is selected at random.
a. Determine P(A), the probability that the return selected shows an AGI under $10K.
b. Find the probability that the return selected shows an AGI between $30K and $100K (i.e., at least $30K but less than $100K).
c. Compute the probability of each of the seven events in the third column of Table 5.21, and record those probabilities in the fourth column.

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Adjusted gross income Under $1OK $10K-under $20K $20K-under $30K S30K-under $40K $40K-under $50K $50K-under $100K 28,801 $100K & over Frequency (1000s) Event Probability 25,352 22,762 18,522 13,940 10,619 14.376 134.372