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Sagot :
Answer:
Step-by-step explanation:
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
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.
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