Probability of Getting Two Sundays in 15 Random Dates

To solve this problem, we need to use the concept of probability. Probability is the measure of the likelihood of an event occurring. In this case, we want to find the probability of getting two Sundays in 15 random dates.

Counting Sundays in 15 Dates

The first step is to count the number of Sundays in 15 random dates. We can use a calendar to do this. If we randomly select 15 dates from a calendar, there are a total of 15 x 7 = 105 possible days we could choose. Out of these 105 days, there are 15 Sundays.

Calculating the Probability

The next step is to calculate the probability of getting two Sundays in 15 random dates. We can use the formula:

P = (nCk) * p^k * (1-p)^(n-k)

where P is the probability, n is the total number of trials, k is the number of successful trials, p is the probability of success, and (1-p) is the probability of failure.

In this case, n = 15, k = 2, p = 15/105 = 1/7, and (1-p) = 6/7. Plugging these values into the formula, we get:

P = (15C2) * (1/7)^2 * (6/7)^13
P = 0.2929

Rounding the answer to two decimal places, we get 0.29.

Choosing the Correct Option

According to the question, we need to select the option that represents the probability of getting two Sundays in 15 random dates. Out of the given options, option A is 0.29, which is the correct answer we obtained through our calculations. Therefore, the correct option is A.

Conclusion

In conclusion, the probability of getting two Sundays in 15 random dates is 0.29 or 29%. To find this probability, we counted the number of Sundays in 15 random dates and used the formula for probability. This problem illustrates how probability can be used to find the likelihood of an event occurring.