In a certain high school, the probability that a student drops out is 0.08, and the probability that a dropout gets a high-school equivalency diploma (GED) is 0.33. What is the probability that a randomly selected student gets a GED?
The probability of both/all events occurring is found by multiplying the probabilities of the individual events.
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00.0235
To find the probability that a randomly selected student gets a GED, we need to calculate the probability that a student both drops out and gets a GED, and then add the probability that a student does not drop out but still gets a GED.
1. Calculate the probability that a dropout gets a GED:
- The probability that a student drops out is given as 0.08.
- The probability that a dropout gets a GED is given as 0.33.
- Multiply these probabilities together to get the probability that a dropout gets a GED:
Probability(dropout and GED) = 0.08 * 0.33 = 0.0264.
2. Calculate the probability that a student does not drop out but still gets a GED:
- The probability that a student does not drop out is equal to 1 minus the probability of dropping out, which would be 1 - 0.08 = 0.92.
- The probability that a student who does not drop out gets a GED is given as 0.33.
- Multiply these probabilities together to get the probability that a student who does not drop out still gets a GED:
Probability(not dropout and GED) = 0.92 * 0.33 = 0.3036.
3. Add the two probabilities together to get the probability that a randomly selected student gets a GED:
Probability(GED) = Probability(dropout and GED) + Probability(not dropout and GED) = 0.0264 + 0.3036 = 0.33.
Therefore, the probability that a randomly selected student gets a GED is 0.33 or 33%.