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Answer:
0.2275 = 22.75% probability that you actually won that round
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
In which
P(B|A) is the probability of event B happening, given that A happened.
is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Fireworks going off
Event B: You won
Probability of fireworks going off.
100% of 1/35 = 0.0286(when you win)
10% of 34/35 = 0.9714(you lost). So
Probability of you winning and fireworks going off:
100% of 1/35, so
If you failed to see the outcome of a round, but you see the fireworks going off, then what is the probability that you actually won that round?
0.2275 = 22.75% probability that you actually won that round