I am not from a quantitative science field and most of the my concepts in probability is rustic.

I came up with this probability question so please forgive me for any error.

**A** and **B** are two tennis doubles player. A and B never played doubles tennis as a team together.

```
Probability of A (with another team mate) winning a doubles game= 0.7
Probability of B (with another team mate) winning a doubles game= 0.5

```

then whats the probability of winning a doubles game with A and B as a team ?

I assumed this is an independent event and I carried out this calculation

```
 p(A and B) = p(A).p(B)
            = 0.7*0.5
            = 0.35

```

Is this calculation correct?
['https://math.stackexchange.com/questions/1742639', 'https://math.stackexchange.com', 'https://math.stackexchange.com/users/23624/']
I think what you need is the probability that they lose, and subtract from $1$. The probability that they both lose (because both of them don't play well) on the same game is $(1-0.5)(1-0.7) = 0.15$, so the probability of the team winning is $1 - 0.15 = 0.85$.

The interpretation of this is the sum of the probabilities of $A$ playing well, but $B$ doesn't (but the team wins), of $B$ playing well but $A$ doesn't (but the team wins anyway), and both $A$ and $B$ play well (the team wins decisively):

$$0.7(1-0.5) + 0.5(1-0.7) + 0.7(0.5) = 0.35 + 0.15 + 0.35 = 0.85.$$

To be fair, this is a bit of an odd problem (not your fault). It requires you to think of the win probabilities of each individual on the team as independent, which in practice is almost certainly *not* the case.
What do you mean by "with another team mate"? Any person at all, as long as it's not A or B? Some particular person? Does it matter who they are playing against? What if A and somebody else are playing against B and somebody else? They can't have probabilities $0.7$ and $0.5$ of winning: the probabilities would have to add to $1$. The question is so vaguely stated that it is impossible to make any sense of it, but certainly it is wrong to multiply the probabilities.