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Answer :
Find the probability of selecting a black checker, replacing it back into the bag, and then selecting another black checker.
When you select one black checker and then replace it back into the bag, the number of checkers in the bag remains the same for the next draw. This is an example of calculating the probability of independent events.
- Probability of selecting a black checker first time: [tex]\frac{10}{20} = \frac{1}{2}[/tex]
- Probability of selecting a black checker second time (after replacing the first one back): [tex]\frac{10}{20} = \frac{1}{2}[/tex]
Since these events are independent when the checker is replaced, the total probability is found by multiplying the individual probabilities:
[tex]\text{Probability} = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4}[/tex]
This would be an example of a(n) _______ (dependent/independent) event.
The correct term is independent event.
Find the probability of selecting a black checker, not replacing it back into the bag, and then selecting another black checker.
When the first checker is not replaced, the total number of checkers in the bag decreases, making this an example of dependent events.
- Probability of selecting a black checker first time: [tex]\frac{10}{20} = \frac{1}{2}[/tex]
- After removing one black checker, 9 black checkers remain and a total of 19 checkers in the bag. The probability of selecting another black checker is then: [tex]\frac{9}{19}[/tex]
Since these events are dependent, the total probability is found by multiplying the probabilities:
[tex]\text{Probability} = \frac{1}{2} \times \frac{9}{19} = \frac{9}{38}[/tex]
This would be an example of a(n) _______ (dependent/independent) event.
The correct term is dependent event.
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