Respuesta :
Answer:
P(x1∩W) = 11/40 = 0.275
the probability of choosing Urn 1 and a white marble is 0.275.
Step-by-step explanation:
Let x1 and x2 represent each urn 1 and 2 respectively,
And R and W represent red and white marbles respectively.
the probability of choosing Urn 1 and a white marble is
P(x1∩W) = P(x1) × P(W in x1) ......1
Where;
P(x1∩W) = the probability of choosing Urn 1 and a white marble
P(x1) = probability of selecting urn 1
P(W in x1) = the probability of choosing white marble in urn1
Since the two urn are of equal probabilities, the probability of choosing urn 1 is half;
P(x1) = 1/2
For urn 1;
Red marbles = 9
White marbles = 11
Total = 20
P(W in urn1) = 11/20
From equation 1;
P(x1∩W) = 1/2 × 11/20 = 11/40
P(x1∩W) = 11/40 = 0.275
the probability of choosing Urn 1 and a white marble is 0.275.
Using conditional probability, it is found that there is a 0.275 = 27.5% probability of choosing Urn 1 and a white marble.
Conditional Probability
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
- P(B|A) is the probability of event B happening, given that A happened.
- [tex]P(A \cap B)[/tex] is the probability of both A and B happening.
- P(A) is the probability of A happening.
In this problem:
- Event A: Urn 1.
- Event B: White marble.
Equally as likely to choose both urns, hence [tex]P(A) = 0.5[/tex].
In urn 1, 11 of the 11 + 9 = 20 marbles are white, hence:
[tex]P(B|A) = \frac{11}{20} = 0.55[/tex]
Applying conditional probability:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
[tex]0.55 = \frac{P(A \cap B)}{0.5}[/tex]
[tex]P(A \cap B) = 0.55(0.5)[/tex]
[tex]P(A \cap B) = 0.275[/tex]
0.275 = 27.5% probability of choosing Urn 1 and a white marble.
A similar problem is given at https://brainly.com/question/14398287
