This might be a very basic question. But I came across a series of studies in which all of them describe the probability of an event happening vs. the probability of that event not happening. Each study has a probability of outcome being a number between $0$ and $1.$ For example, probabilities of events in study $A$ are $0.043,$ Study $B$ $0.214,$ study $C$ $0.00,$ study $D$ $0.105.$
Would it be correct to obtain a mean probability with this formula $(A+B+C+D)/4$ and how could I get a standard deviation from each study and the total?
The only data available on the studies is the number of participants is $N$, events and odds ratio with a $95\%$ CI comparing treatments.