i just can’t understand this i know the eq is P(at least one)= 1-P(all occur) but every time i do the problems i get them wrong ??? like for some reason the equation changes my teacher has tried to explain it but i just don’t get it
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In statistics, the probability of at least one event occurring is calculated by adding the probabilities of all the individual events that can occur and then subtracting the probability that none of the events will occur. This is known as the “inclusive or” rule, and it can be expressed mathematically as:
P(at least one event) = P(event 1) + P(event 2) + … + P(event n) – P(no events)
For example, suppose you have a bag containing three red balls and two blue balls, and you want to calculate the probability of drawing at least one red ball if you draw two balls from the bag without replacement. The probability of drawing at least one red ball is calculated as follows:
P(at least one red ball) = P(red ball 1) + P(red ball 2) – P(no red balls)
= (3/5) + (2/4) – (2/5)
= (9/10) – (2/5)
= (36/50) – (24/50)
= 12/50
= 0.24
This means that there is a 24% chance of drawing at least one red ball if you draw two balls from the bag without replacement.
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