Respuesta :
Answer:
The probability that both marbles are green is [tex]\bf\displaystyle\frac{1}{28}[/tex].
Step-by-step explanation:
To find the probability of drawing 2 green marbles, we create 2 events where:
- A = 1st marble is green
- B = 2nd marble is green
Hence, the event of drawing 2 green marbles on both 1st and 2nd is P(A and B) or P(A∩B).
Since the outcome of event B depends on event A, then these events are dependent events (conditional probability), where:
[tex]\boxed{P(A\cap B)=P(A)\times P(B|A)}[/tex]
Event A:
- Total number of marbles [tex](n(S)_A)[/tex] = 3 + 2 + 2 + 1 = 8
- Total number of green marble [tex](n(A))[/tex] = 2
[tex]\displaystyle P(A)=\frac{n(A)}{n(S)_A}[/tex]
[tex]\displaystyle =\frac{2}{8}[/tex]
Event B:
- Total number of marbles [tex](n(S)_B)[/tex] = 8 - 1 = 7 (1 marble was taken at event A)
- Total number of green marbles [tex](n(B))[/tex] = 2 - 1 = 1 (1 green marble was taken at event A)
[tex]\displaystyle P(B|A)=\frac{n(B)}{n(S)_B}[/tex]
[tex]\displaystyle =\frac{1}{7}[/tex]
Therefore:
[tex]P(A\cap B)=P(A)\times P(B|A)[/tex]
[tex]\displaystyle=\frac{2}{8} \times\frac{1}{7}[/tex]
[tex]\bf\displaystyle=\frac{1}{28}[/tex]
