of 53 plays attributed to a playwright, 16 are comedies, 18 are tragedies, and 19 are histories. if one play is selected at random, find the odds against selecting a tragedy.
To find the odds against selecting a tragedy, we need to determine the number of plays that are not tragedies and compare it to the total number of plays.
The number of plays that are not tragedies is the sum of comedies and histories:
Number of plays that are not tragedies = Number of comedies + Number of histories
= 16 + 19
= 35
The total number of plays is equal to the sum of all three categories:
Total number of plays = Number of comedies + Number of tragedies + Number of histories
= 16 + 18 + 19
= 53
Therefore, the odds against selecting a tragedy can be expressed as: number of plays that are not tragedies : number of total plays = 35 : 53.
To find the odds against selecting a tragedy, we need to determine the number of unfavorable outcomes (not selecting a tragedy) and the number of favorable outcomes (selecting a tragedy).
Given that there are 53 total plays, and 18 of them are tragedies, we can calculate the unfavorable outcomes by subtracting the number of tragedies from the total number of plays:
Unfavorable Outcomes = Total Plays - Tragedies = 53 - 18 = 35
Since the question asks for the odds against selecting a tragedy, we use the following formula to calculate the odds against an event:
Odds against an event = Unfavorable Outcomes / Favorable Outcomes
In this case, the number of favorable outcomes (selecting a tragedy) is 18. Therefore, the odds against selecting a tragedy are:
Odds against selecting a tragedy = 35 / 18
Hence, the odds against selecting a tragedy are 35 to 18, or simply 35/18.
the prob of selecting a tragedy = 18/53
prob of not section a tragedy = 35/53
odds against selecting a tragedy
= (35/53 / (18/53+
= 35 : 18