probability and ratio

There are 200 beads in a bag and one is selected at random, it's color is written down and then the bead is put back in.
They do that twice.
The probability of getting a red twice is 0:1369.

i really dont understand this question. ive been told by my classmates that it may have something to do with probability tree diagrams and square roots.

i am so confused, can anybody help?

Reply 1

SomeonesDad

How many different colours are there? Does it tell you, or is that what you're looking to solve?

(edited 1 year ago)

Reply 2

mosaurlodon

Im assuming you meant 0.1369

lets call the number of red beads in the bag R, so the probability of picking a red bead out of 200 beads is R/200

they do this twice so the probability is (R/200)^2

now the "The probability of getting a red twice is 0.1369." so (R/200)^2 = 0.1369 and solve for R.

Reply 3

SomeonesDad

Right, I've found the original question:
A bag contains 200 beads. Some of the beads are red. A bead is selected at random. Its colour is recorded and then the bead is replaced. A second bead is selected at random and its colour is also recorded. The probability that two red beads are selected is 0·1369. Calculate the number of red beads in the bag.

Answer:
The probability of the exact same thing happening twice (and it is the same thing here as the ball is put back in the bag, not kept out) is the Probability of it happening once multiplied by the Probability of it happening once.

So, it's P1 x P1 = P1 Squared

We know that P1 Squared = 0.1369
The probability of it happening once is SQRT 0.1369
My calculator tells me this is 0.37
0.37 is the same as saying 37% or 37 times in each 100
You've got twice as many as 100. i.e. 200 balls so you have 2 x 37 = 74 balls out of the 200 are red.