Complete the following:
i. Calculate the probability of the desired event, rounded to 3 significant digits as needed.
ii. Calculate the probability of the complementary event.
iii. Compute the odds against and odds in favour of the event.
Rolling a number less than 3 on a 12-sided die.
Probability of Event:
Round to 3 significant digits.
Probability of the Complement of the Event:
Round to 3 significant digits.
Odds Against the Event:
:
Odds In Favour of the Event:
:
Express ratios in lowest terms.
i. Calculate the probability of the desired event:
There are 2 numbers less than 3 on a 12-sided die, which are 1 and 2. Therefore, the probability of rolling a number less than 3 is 2/12 = 1/6, rounded to 3 significant digits as needed is approximately 0.167.
ii. Calculate the probability of the complementary event:
The complementary event is rolling a number that is 3 or higher on a 12-sided die. There are 10 numbers that are 3 or higher on a 12-sided die. Therefore, the probability of rolling a number that is 3 or higher is 10/12 = 5/6, rounded to 3 significant digits as needed is approximately 0.833.
iii. Compute the odds against and odds in favour of the event:
Odds Against the Event:
To calculate the odds against the event, we divide the probability of the complementary event by the probability of the event.
Odds against = (5/6) / (1/6) = 5
Odds In Favour of the Event:
To calculate the odds in favour of the event, we divide the probability of the event by the probability of the complementary event.
Odds in favour = (1/6) / (5/6) = 1/5
Therefore, the odds against the event are 5:1, and the odds in favour of the event are 1:5. Expressing these ratios in lowest terms, we get the odds against as 5:1 and the odds in favour as 1:5.