Respuesta :
Answer:
The probability that both Jolly Ranchers will be watermelon is [tex]\displaystyle\bf \frac{77}{1335}[/tex].
Step-by-step explanation:
To find the probability of taking 2 watermelons, we create 2 events where:
- A = 1st Jolly Rancher is watermelon
- B = 2nd Jolly Rancher is watermelon
Hence, the event of taking 2 watermelons 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 Jolly Ranchers [tex](n(S)_A)[/tex] = 35 + 22 + 18 + 15 = 90
- Total number of watermelon [tex](n(A))[/tex] = 22
[tex]\displaystyle P(A)=\frac{n(A)}{n(S)_A}[/tex]
[tex]\displaystyle =\frac{22}{90}[/tex]
Event B:
- Total number of marbles Jolly Ranchers [tex](n(S)_B)[/tex] = 90 - 1 = 89 (1 Jolly Rancher was taken at event A)
- Total number of watermelon [tex](n(B))[/tex] = 22 - 1 = 21 (1 watermelon was taken at event A)
[tex]\displaystyle P(B)=\frac{n(B)}{n(S)_B}[/tex]
[tex]\displaystyle =\frac{21}{89}[/tex]
Therefore:
[tex]P(A\cap B)=P(A)\times P(B|A)[/tex]
[tex]\displaystyle=\frac{22}{90} \times\frac{21}{89}[/tex]
[tex]\displaystyle=\bf \frac{77}{1335}[/tex]
