Of 43 plays attributed to a playwright 16 are comedies, 15 are tragedies, 12 are histories. If one play is selected random find the odds against selecting a history?
To find the odds against selecting a history, we need to calculate the probability of not selecting a history.
Given that there are a total of 43 plays, we can represent the total sample space as 43.
The number of histories is given as 12. Therefore, the probability of selecting a history is 12/43.
To find the probability of not selecting a history, we subtract the probability of selecting a history from 1 (since the sum of all probabilities adds up to 1):
1 - (12/43) = 31/43
So, the probability of not selecting a history is 31/43.
To express this as odds against selecting a history, we need to compare the probability of not selecting a history to the probability of selecting a history (12/43):
Odds against selecting a history = (probability of not selecting a history) / (probability of selecting a history)
Odds against selecting a history = (31/43) / (12/43) = 31/12
Therefore, the odds against selecting a history are 31 to 12, or simply 31:12.
To find the odds against selecting a history play, we need to determine the number of plays that are not history plays and compare it to the number of history plays.
The total number of plays attributed to the playwright is 43.
Since there are 12 history plays, the number of plays that are not history plays would be 43 - 12 = 31.
Therefore, the odds against selecting a history play would be 31:12, or simply 31/12.