diff --git a/torchvision/transforms/transforms.py b/torchvision/transforms/transforms.py
index 38fc417204c..1117b6c555f 100644
--- a/torchvision/transforms/transforms.py
+++ b/torchvision/transforms/transforms.py
@@ -489,24 +489,42 @@ def __repr__(self) -> str:
         return f"{self.__class__.__name__}()"
 
 
-class RandomTransforms:
-    """Base class for a list of transformations with randomness
+class RandomApply(torch.nn.Module):
+    """Apply randomly a list of transformations with a given probability.
+
+    .. note::
+        In order to script the transformation, please use ``torch.nn.ModuleList`` as input instead of list/tuple of
+        transforms as shown below:
+
+        >>> transforms = transforms.RandomApply(torch.nn.ModuleList([
+        >>>     transforms.ColorJitter(),
+        >>> ]), p=0.3)
+        >>> scripted_transforms = torch.jit.script(transforms)
+
+        Make sure to use only scriptable transformations, i.e. that work with ``torch.Tensor``, does not require
+        `lambda` functions or ``PIL.Image``.
 
     Args:
-        transforms (sequence): list of transformations
+        transforms (sequence or torch.nn.Module): list of transformations
+        p (float): probability
     """
 
-    def __init__(self, transforms):
+    def __init__(self, transforms, p=0.5):
+        super().__init__()
         _log_api_usage_once(self)
-        if not isinstance(transforms, Sequence):
-            raise TypeError("Argument transforms should be a sequence")
         self.transforms = transforms
+        self.p = p
 
-    def __call__(self, *args, **kwargs):
-        raise NotImplementedError()
+    def forward(self, img):
+        if self.p < torch.rand(1):
+            return img
+        for t in self.transforms:
+            img = t(img)
+        return img
 
     def __repr__(self) -> str:
         format_string = self.__class__.__name__ + "("
+        format_string += f"\n    p={self.p}"
         for t in self.transforms:
             format_string += "\n"
             format_string += f"    {t}"
@@ -514,16 +532,16 @@ def __repr__(self) -> str:
         return format_string
 
 
-class RandomApply(torch.nn.Module):
-    """Apply randomly a list of transformations with a given probability.
+class RandomOrder(torch.nn.Module):
+    """Apply a list of transformations in a random order.
 
     .. note::
         In order to script the transformation, please use ``torch.nn.ModuleList`` as input instead of list/tuple of
         transforms as shown below:
 
-        >>> transforms = transforms.RandomApply(torch.nn.ModuleList([
+        >>> transforms = transforms.RandomOrder(torch.nn.ModuleList([
         >>>     transforms.ColorJitter(),
-        >>> ]), p=0.3)
+        >>> ]))
         >>> scripted_transforms = torch.jit.script(transforms)
 
         Make sure to use only scriptable transformations, i.e. that work with ``torch.Tensor``, does not require
@@ -531,25 +549,21 @@ class RandomApply(torch.nn.Module):
 
     Args:
         transforms (sequence or torch.nn.Module): list of transformations
-        p (float): probability
     """
 
-    def __init__(self, transforms, p=0.5):
+    def __init__(self, transforms):
         super().__init__()
         _log_api_usage_once(self)
         self.transforms = transforms
-        self.p = p
 
     def forward(self, img):
-        if self.p < torch.rand(1):
-            return img
-        for t in self.transforms:
-            img = t(img)
+        order = torch.randperm(len(self.transforms))
+        for i in order:
+            img = self.transforms[i.item()](img)
         return img
 
     def __repr__(self) -> str:
         format_string = self.__class__.__name__ + "("
-        format_string += f"\n    p={self.p}"
         for t in self.transforms:
             format_string += "\n"
             format_string += f"    {t}"
@@ -557,32 +571,50 @@ def __repr__(self) -> str:
         return format_string
 
 
-class RandomOrder(RandomTransforms):
-    """Apply a list of transformations in a random order. This transform does not support torchscript."""
+class RandomChoice(torch.nn.Module):
+    """Apply single transformation randomly picked from a list.
 
-    def __call__(self, img):
-        order = list(range(len(self.transforms)))
-        random.shuffle(order)
-        for i in order:
-            img = self.transforms[i](img)
-        return img
+    .. note::
+        In order to script the transformation, please use ``torch.nn.ModuleList`` as input instead of list/tuple of
+        transforms as shown below:
 
+        >>> transforms = transforms.RandomChoice(torch.nn.ModuleList([
+        >>>     transforms.ColorJitter(),
+        >>> ]), p=torch.Tensor([0.3]))
+        >>> scripted_transforms = torch.jit.script(transforms)
 
-class RandomChoice(RandomTransforms):
-    """Apply single transformation randomly picked from a list. This transform does not support torchscript."""
+        Make sure to use only scriptable transformations, i.e. that work with ``torch.Tensor``, does not require
+        `lambda` functions or ``PIL.Image``.
+
+    Args:
+        transforms (sequence or torch.nn.Module): list of transformations
+        p (optional, torch.Tensor): input tensor containing weights. Default: equal weights
+    """
 
-    def __init__(self, transforms, p=None):
-        super().__init__(transforms)
-        if p is not None and not isinstance(p, Sequence):
-            raise TypeError("Argument p should be a sequence")
+    def __init__(self, transforms, p: Optional[torch.Tensor] = None):
+        super().__init__()
+        _log_api_usage_once(self)
+        if p is None:
+            p = torch.ones(len(transforms))
+        self.transforms = transforms
         self.p = p
 
-    def __call__(self, *args):
-        t = random.choices(self.transforms, weights=self.p)[0]
-        return t(*args)
+    def forward(self, img):
+        i = torch.multinomial(self.p, 1)
+        # self.transforms[i.item()](img) gives Error: Expected integer literal for index, whilw JIT Scripting
+        # Workaround the ModuleList indexing issue: https://github.com/pytorch/pytorch/issues/16123
+        for j,t in enumerate(self.transforms):
+            if i==j:
+                return t(img)
 
     def __repr__(self) -> str:
-        return f"{super().__repr__()}(p={self.p})"
+        format_string = self.__class__.__name__ + "("
+        format_string += f"\n    p={self.p}"
+        for t in self.transforms:
+            format_string += "\n"
+            format_string += f"    {t}"
+        format_string += "\n)"
+        return format_string
 
 
 class RandomCrop(torch.nn.Module):