Find the indicated probability. A box contains 20 blue marbles, 18 green marbles, and 12 red marbles. Two marbles are selected at random without replacement. Let E be the event where the first marble selected is green. Let F be the event that the second marble selected is green. Find P(F|E).

To find the probability of event F (selecting a green marble second) given event E (selecting a green marble first), we use the formula for conditional probability:

1. Calculate the probability of event F and E occurring together (P(F ∩ E)):

- P(E) = Probability of selecting a green marble first =

- After selecting a green marble, there are 17 green marbles left out of 49 marbles total.

- Therefore, P(F ∩ E) = Probability of selecting a green marble first and then a green marble second =

17/49

jimthompson5910 jimthompson5910 · Answer 2 · 2024-06-07T05:02:05-04:00

Answer: 17/49

Explanation

The vertical bar represents the key term "given" which is used in conditional probability.

P(F | E) = P(F given E)

I prefer the second version since the vertical bar could easily be confused with the uppercase letter 'i' or lowercase L or the digit 1. Of course it's up to you which you prefer best.

P(F given E) is where we ask "what is P(F) if we know 100% that event E has occurred?"

E in this case represents "first marble is green".

18 green drops to 18-1 = 17 remaining green

The 20+18+12 = 50 total marbles drops to 50-1 = 49 total marbles.

P(F given E) = 17/49 since we have 17 remaining green out of 49 remaining total marbles.

Using a calculator we find this approximation 17/49 ≈ 0.3469 meaning there's roughly a 34.69% chance of event F occurring if we know that event E has already occurred.