prob and odds

Question

The odds in favor of an event occurring are 1 to 7.  Find the probability of the event not occurring

 

Answer 1

the odds in favor of an event are 1 to 7

this means the event occurs 1 time for every 7 times it does not occur

the probability that the event occurs is 1/8

the probability that the event does not occur is 7/8

if you roll a die the odds of rolling a 3 is 1 to 5  (there is one 3 and five other numbers that can occur)

the probability of rolling a 3 is 1/6  (one 3 out of a total of 6 numbers)

the probability of not rolling a 3 is 5/6

 

Answer 2

The odds are calculated like this: (times an event happens)/ (times an event does NOT happen). 

In this example we have 7 + 1 = 8 total trials, where the event happened once, and didn't happen 7 times.

 

Probability is calculated like this: (the number of times an event happened)/ (the total number of trials).

In this problem, they are asking for the probability that the event did NOT happen.  Out of the 8 trials, the event did NOT happen 7 times.

 

So the answer is calculated by (the number of times the event did NOT happen)/ (the total number of trials) = 7/8