caggh345
18.05.2021 •
Mathematics
Can someone please help
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Ответ:
Ответ:
Ответ:
P ( A / E ) = 0.6365
Step-by-step explanation:
Given:
- Urn A : 2 White , 4 Red
- Urn B : 8 White , 4 Red
- Urn C : 1 White , 3 Red
- White = W , Red = R
Find
If 1 ball is selected from each urn, what is the probability that the ball chosen from urn Awas white given that exactly 2 white balls were selected?
Solution:
- Let event E be selecting exactly 2 white balls after going through each urn.
- The possible outcomes for event E can be expressed as:
{ ( W , W , R ) : ( W , R , W ) : ( R , W , W ) }
- The probability of event E would be as such:
P ( E ) = P ( W , W , R ) + P( W , R , W ) + P ( R , W , W )
P ( E ) = ( 2/6 * 8/12 * 3/4 ) + ( 2/6 * 4/12 * 1/4 ) + ( 4/6 * 8/12 * 1/4 )
P ( E ) = 0.1667 + 0.0278 + 0.11111
P ( E ) = 0.30561
- Let event A be selecting a white ball from urn A and exactly two white balls in total are picked:
P ( A & E ) = P ( W , W , R ) + P( W , R , W )
P ( A & E ) = ( 2/6 * 8/12 * 3/4 ) + ( 2/6 * 4/12 * 1/4 )
P ( A & E ) = 0.1667 + 0.0278
P ( A & E ) = 0.1944
- The conditional probability of choosing a white ball from urn A given that exactly 2 W balls are selected among three urns:
P ( A / E ) = P ( A & E ) / P ( E )
P ( A / E ) = 0.1944 / 0.30561
P ( A / E ) = 0.6365