Respuesta :
Answer:
60/220
Step-by-step explanation:
we use combination,
[tex] (\frac{5}{1} ) \times ( \frac{4}{1} ) \times ( \frac{3}{1} )[/tex]
[tex]5 \times 4 \times 3 = 60[/tex]
then, all divided by,
[tex] (\frac{12}{3}) = 220 [/tex]
[tex]60 \div 220[/tex]
The probability of the first piece being milk chocolate, the second being white chocolate, and the third being milk chocolate is 0.06.
What is Probability?
The probability helps us to know the chances of an event occurring.
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
The sample contains five milk chocolates, three dark chocolates, and four white chocolates. Therefore, the probability that the first piece is milk chocolate is
[tex]\rm Probability=\dfrac{\text{Number of Milk choclates}}{\text{Total number of choclates}}[/tex]
[tex]\rm Probability=\dfrac{5}{12}[/tex]
Now, since the chocolate is been eaten the sample size will reduce from 12 chocolates in total to 11 chocolates in total (four milk chocolates, three dark chocolates, and four white chocolates). Therefore, the probability of the second piece being white chocolate is
[tex]\rm Probability=\dfrac{\text{Number of White choclates}}{\text{Total number of choclates}}[/tex]
[tex]\rm Probability=\dfrac{4}{11}[/tex]
Now, as the chocolate is been eaten the sample size will reduce from 11 chocolates in total to 10 chocolates in total (four milk chocolates, three dark chocolates, and three white chocolates). Therefore, the probability of the third piece being milk chocolate is
[tex]\rm Probability=\dfrac{\text{Number of Milk choclates}}{\text{Total number of choclates}}[/tex]
[tex]\rm Probability=\dfrac{4}{10}[/tex]
Thus, the probability of the first piece being milk chocolate, the second being white chocolate, and the third being milk chocolate is
[tex]\rm Probability=\dfrac{5}{12}\times \dfrac{4}{11} \times \dfrac{4}{10} = \dfrac{80}{1320} = 0.06[/tex]
Hence, the probability of the first piece being milk chocolate, the second being white chocolate, and the third being milk chocolate is 0.06.
Learn more about Probability:
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