The ACE Recording Studio has a new client visiting Orlando in the upcoming weeks. A new and upcoming band wants to offer a free concert in one of the venues around town. Currently, there are 10

venues that will allow this kind of event for the community. Each of the venues is willing to offer the concert on either Monday, Tuesday or Wednesday of the first 2
weeks of the month. What are the odds of booking the concert on a Monday?
A. 1:3
B. 3:4
C. 6:54
D. 6:60
E. 1:2
F. 20:60
G. 1:14
Best answer

1 answer

To find the odds of booking the concert on a Monday, we need to consider the total possible options for booking and the favorable options for booking on Monday.

  1. Total Venues: 10 venues
  2. Days available for booking: Monday, Tuesday, and Wednesday (3 days)
  3. Weeks available: The first 2 weeks of the month (2 weeks)

Given that each venue can offer a concert on one of the 3 days across 2 weeks, this gives:

  • Total possible concert slots = 10 venues × 3 days/week × 2 weeks = 60 possible concert slots.
  1. Favorable outcomes for booking on a Monday:
    • There are 10 venues, and for each venue, there is 1 favorable day (Monday) in each of the 2 weeks, so:
    • Total favorable slots for Monday = 10 venues × 2 weeks = 20 favorable outcomes.

Now, the odds of an event are calculated using the formula:

\[ \text{Odds} = \frac{\text{Favorable Outcomes}}{\text{Unfavorable Outcomes}} \]

  1. Unfavorable outcomes (for Tuesday and Wednesday):
    • Total options excluding Monday = 10 venues × 2 days/week × 2 weeks = 40 unfavorable outcomes.

Thus, the odds of booking the concert on a Monday are:

\[ \text{Odds} = \frac{20}{40} = 1:2 \]

Therefore, the best answer is E. 1:2.