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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You’ve made a small mistake. Probably of “at least 1” is actually 100% – the probability of none. `P(at least one) = 1 – P(none)`
Just because the probability of “none” tends to be easiest to figure out, especially since it’s a single goal to calculate, this equation tends to be easiest to work with.
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.
Let’s boil it down to very simple terms. Let’s say there’s two girls you want to ask out, Amy and Beth. You think there’s a 40% chance Amy will say yes, and a 30% chance Beth will say yes. Maybe both say yes, maybe both say no. You can go out with both of them, if they both happen to say yes. What’s the probability you’ll have a date this weekend?
To get the answer, you have to figure out the probability of them both saying no. There’s a 60% chance Amy says no, and a 70% chance Beth says no. 60% x 70% = 42% chance of two no’s.
So since there’s a 42% chance of no dates, that means the chance of at least one date is just 100 minus that, or 58%.
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