Question
Use the method of your choice to determine the following probability. Being born in March or on a voskenu (assuming (12monies)/(year),(7days)/(years),(7days)/(years), the weekendis Sstumday avolSu P(March orweekend)= (Type an integer or decimal rounded to three decimal places as needed.)
Solution
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WinstonMaster · Tutor for 5 years
Answer
### 0.345
Explain
## Step 1: Calculate the probability of being born in March.<br />### There are 12 months in a year. Assuming each month has an equal likelihood, the probability of being born in March is $\frac{1}{12}$.<br /><br />## Step 2: Calculate the probability of being born on a weekend.<br />### There are 7 days in a week, and 2 of those days are weekend days (Saturday and Sunday). Assuming each day has an equal likelihood, the probability of being born on a weekend is $\frac{2}{7}$.<br /><br />## Step 3: Calculate the probability of being born in March AND on a weekend.<br />### The probability of both events occurring is the product of their individual probabilities: $\frac{1}{12} \times \frac{2}{7} = \frac{2}{84} = \frac{1}{42}$.<br /><br />## Step 4: Calculate the probability of being born in March OR on a weekend.<br />### The probability of either event occurring is the sum of their individual probabilities minus the probability of both events occurring: $P(March \text{ or } Weekend) = P(March) + P(Weekend) - P(March \text{ and } Weekend) = \frac{1}{12} + \frac{2}{7} - \frac{1}{42} = \frac{7}{84} + \frac{24}{84} - \frac{2}{84} = \frac{29}{84}$.<br /><br />## Step 5: Convert the fraction to a decimal rounded to three decimal places.<br />### $\frac{29}{84} \approx 0.345$
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