The probability of Joe contracting an STD at least once over 4 sexual encounters, given a 1 in 4 chance per encounter, can be calculated using the complementary probability method. The complementary event is not contracting an STD in any of the encounters, which has a probability of 3/4 for each encounter. Therefore, the probability of not contracting an STD in all 4 encounters is (3/4)^4, resulting in a probability of 1 - (3/4)^4 for contracting an STD at least once, which equals approximately 0.683. This confirms that Joe has a 68.3% chance of contracting an STD after 4 encounters.
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helpmepleasezz said:Homework Statement
There is a 1 in 4 chance that on any given sexual encounter, Joe will contract an STD. If Joe has sex 4 times, what are the chances of him having an STD?
Homework Equations
Something with combinations maybe?
The Attempt at a Solution
I thought you would just add up the probability of the event happening for each trial, but that would give me 100% which isn't right.