Maths help! Probability

[missk167]

Maths question eek, I am doing my level 5 in healthcare and social and have to do my maths; which I really struggle with. Any help would be amazing.

Angela has four hats, each style is available in four colours - red, black, white and green. If she randomly selects 4 hats, 1 from each style, what is the probability that she will choose all red hats? Give your answer as a fraction?

Part 2

Give your answer as a decimal to 3 decimal places.

Katie

Hopefully the picture has added. I’m not great at probability but I do love a probability tree.

If she picks one hat there is a 1in 4 chance it is red (R) and 3 in 4 chance it is not red (NR).

If she picks two then the second choice on its own is the same odds so we multiply the probabilities together as they are exclusive if each other (ie getting red the first time doesn’t affect whether you get red the second time)

And so on for hat 3&4

Assuming she has one hat of each of 4 colours in each style (let's say beret, fedora, bowler, bobble), then she has a 1/4 chance of picking a red beret, a 1/4 chance of picking a red fedora, 1/4 chance of picking a red bowler and 1/4 chance of picking a red bobble hat.

That gives 1/4 x 1/4 x 1/4 x 1/4 = 1/256

1/256 = 0.00390625, or 0.004 to three decimal places.

Does that make any sense?

I haven't done maths since I was 16 but delighted to have arrived at same answer as the posters above 🤣

@GunsNShips

Hopefully the picture has added. I’m not great at probability but I do love a probability tree.

If she picks one hat there is a 1in 4 chance it is red (R) and 3 in 4 chance it is not red (NR).

If she picks two then the second choice on its own is the same odds so we multiply the probabilities together as they are exclusive if each other (ie getting red the first time doesn’t affect whether you get red the second time)

And so on for hat 3&4

Loving the whiteboard. 🤣

Arrrgh - did the hard bit, didn’t round properly

Thank you so much everyone that was so helpful.

Thank you
Katie