Question

Below is the probability of three independent events happening

Find the probability that at least one of these Events happens.

Round your answer to two decimal places.

Event 1: $0.56$, Event 2:$0.38$, Event 3:$0.67$?

Answer 1

Probability of at least one of the three Events to happen:

The probability of at least one event happening is $1$ minus probability of the none of event happen.

That is:

$P\left(\text{Atleast}1\right)=1-P\left(\text{None}\right)$

Given the probability of event happening is Event 1: $0.56$, Event 2: $0.38$, Event 3: $0.67$.

Thus, the probability of not happening of the Event 1: $\left(1-0.56\right)=0.44$, Event 2: $\left(1-0.38\right)=0.62$, Event 3: $\left(1-0.67\right)=0.33$.

Since the events are independent, the probability of none of the happen is $0.44\times 0.62\times 0.33=0.09$.

Now, find the probability of at least one of the event happening by subtracting the probability of none of event happening from one.

$$\begin{gathered} P\left(\text{Atleast one Event Happen}\right)=1-0.09 \\ =0.91 \end{gathered}$$

Hence, the probability of happening of at least one event is $0.91$.