Is Haskell's mapM not lazy?

UPDATE: Okay this question becomes potentially very straightforward.

q <- mapM return [1..]

Why does this never return?

Does mapM not lazily deal with infinite lists?

The code below hangs. However, if I replace line A by line B, it doesn't hang anymore. Alternatively, if I preceed line A by a "splitRandom $", it also doesn't hang.

Q1 is: Is mapM not lazy? Otherwise, why does replacing line A with line B "fix this" code?

Q2 is: Why does preceeding line A with splitRandom "solve" the problem?

import Control.Monad.Random
import Control.Applicative

f :: (RandomGen g) => Rand g (Double, [Double])
f = do
    b <- splitRandom $ sequence $ repeat $ getRandom
    c <- mapM return b -- A
    -- let c = map id b -- B
    a <- getRandom
    return (a, c)

splitRandom :: (RandomGen g) => Rand g a -> Rand g a
splitRandom code = evalRand code <$> getSplit

t0 = do
    (a, b) <- evalRand f <$> newStdGen
    print  a
    print (take 3 b)

The code generates an infinite list of random numbers lazily. Then it generates a single random number. By using splitRandom, I can evaluate this latter random number first before the infinite list. This can be demonstrated if I return b instead of c in the function.

However, if I apply the mapM to the list, the program now hangs. To prevent this hanging, I have to apply splitRandom again before the mapM. I was under the impression that mapM can lazily