A date in the month of June is chosen at random. Find the probability of the event of the​ date's being each of the following.

a. June 16                b. June 31                c. Before June 20
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Part 1
a. The probability of the event of the​ date's being June 16 is
  
enter your response here.
​(Type an integer or a simplified​ fraction.)

1 answer

To find the probability of a specific date in June, we need to understand that June has 30 days. Therefore, each date in June has an equal probability of being chosen.

a. The probability of the event of the date being June 16:

  • There is only 1 specific date (June 16).
  • The total number of days in June is 30.

The probability \( P \) of choosing June 16 is given by:

\[ P(\text{June 16}) = \frac{1}{30} \]

b. The probability of the event of the date being June 31:

  • June only has 30 days, so June 31 does not exist.
  • Thus, the probability \( P \) of choosing June 31 is:

\[ P(\text{June 31}) = 0 \]

c. The probability of the event of the date being before June 20:

  • The dates before June 20 are June 1 to June 19, which totals 19 days.
  • Therefore, the probability \( P \) of choosing a date before June 20 is given by:

\[ P(\text{Before June 20}) = \frac{19}{30} \]

In summary:

  • a. \( P(\text{June 16}) = \frac{1}{30} \)
  • b. \( P(\text{June 31}) = 0 \)
  • c. \( P(\text{Before June 20}) = \frac{19}{30} \)