Answer :
The events "a red checker is selected, not replaced, and then a black checker is selected" are dependent.
- The events are dependent because the outcome of the first event (selecting a red checker) affects the probability of the second event (selecting a black checker).
- To find the probability, we need to consider the probability of each event separately and then multiply them together.
- Probability of selecting a red checker: [tex]\( \frac{15}{25} \)[/tex] (because there are 15 red checkers out of 25 total)
- After selecting a red checker, there are now 24 checkers left in the bag, with 10 of them being black.
- Probability of selecting a black checker after selecting a red one: [tex]\( \frac{10}{24} \)[/tex] (because there are 10 black checkers out of 24 remaining checkers)
- Multiply the probabilities of the two events together to find the overall probability: [tex]\( \frac{15}{25} \times \frac{10}{24} \)[/tex]
Calculating the probability:
[tex]\( \frac{15}{25} \times \frac{10}{24} = \frac{3}{5} \times \frac{5}{12} = \frac{1}{4} \)[/tex]
Therefore, the probability of selecting a red checker, not replacing it, and then selecting a black checker is [tex]\( \frac{1}{4} \).[/tex]
Complete Question: Determine whether the events "a red checker is selected, not replaced, and then a black checker is selected" are independent or dependent, and find the probability.
