A Level maths help needed!!!

The probability that a light bulb in a pack of 10 is faulty is 0.05, 0.95 that it isn't faulty.
Work out the probability that at there will be at least 1 faulty bulb.
I know you have the times (0.95) to the power of 10, but I don't understand why you then take the answer away from 1.

Let X denote the number of faulty light bulbs:

The probability that there is atleast one faulty bulb means we determine:

Prob that exactly one is faulty... P(X=1)
Prob that exactly two are faulty... P(X=2)
Prob that exactly three are faulty... P(X=3)
...
Prob that exactly 10 are faulty... P(X=10)

Then add them up. Hence, this probability is P(X=1) + ... + P(X=10).

But in the sample space, there is one more event that could occur: no light bulbs are faulty, in other words there is also P(X=0) that we ignore.

By the fundamental rule in probability, all these probabilities must sum to 1.

Hence,

P(X=0) + P(X=1) + ... + P(X=10) = 1

subtract P(X=0) from both sides and we have

P(X=1) + ... + P(X=10) = 1 - P(X=0)

and so our answer is quite simply equivalent to determining 1-P(X=0). Hence why you take that answer away from 1.

The probability that a light bulb in a pack of 10 is faulty is 0.05, 0.95 that it isn't faulty.
Work out the probability that at there will be at least 1 faulty bulb.
I know you have the times (0.95) to the power of 10, but I don't understand why you then take the answer away from 1.

The probability that a light bulb in a pack of 10 is faulty is 0.05, 0.95 that it isn't faulty.
Work out the probability that at there will be at least 1 faulty bulb.
I know you have the times (0.95) to the power of 10, but I don't understand why you then take the answer away from 1.

If you do (0.05)^10 then you don't have to take it away from 1