Probability of getting 4 white beads

[juls]

Bag A contains 6 white beads and 3 black beads. Bag B contains 6 white beads and 4 black beads. One bead is chosen at random from each bag. A second bead is chosen at random from each bag. Find the probability that, all four beads are white.

I am not sure if the answer is P(WWWW), in which case we use multiplication, or P (ww) and P2 (WW).

i think the answer is (6/9 X 5/8) + (6/10 X 5/9) = 0.75
but there's a chance it might be (6/9 *5/8 *6/10 *5/9)

I NEED HELP!

 

[arildno]

Remember that whatever your result from drawing two beads from bag A is INDEPENDENT from drawing two beads from bag B.

 

[tacman]

The correct answer is (6/9 *5/8 *6/10 *5/9) = 0.1852. This is because when selecting the first bead, there is a 6/9 chance of selecting a white bead from Bag A and a 6/10 chance of selecting a white bead from Bag B. Then, when selecting the second bead, there is a 5/8 chance of selecting a white bead from Bag A and a 5/9 chance of selecting a white bead from Bag B. We multiply these probabilities together to get the overall probability of selecting 4 white beads from both bags. So, the probability of getting 4 white beads is 0.1852 or approximately 18.52%.

In this situation, it is important to use multiplication because we are looking for the probability of two independent events occurring together (selecting a white bead from each bag twice). When we are looking for the probability of one event OR another event occurring, we use addition.

I hope this helps clarify any confusion. Remember, it is always important to carefully read the question and consider if we are looking for the probability of one event or multiple events occurring.