P(B/A) is [tex]\frac{5}{9}[/tex] in the simplest form
Step-by-step explanation:
Let us explain how to solve the problem
- P(B|A) is called the "Conditional Probability" of B given A
- Conditional probability is the probability of one event occurring with some relationship to one or more other events that means event A has already happened, now what is the chance of event B
- The formula for conditional probability is P(B|A) = P(A and B)/P(A), where P(A and B) is P(A) . P(B given A occurred)
∵ There are 3 red marbles, 5 green marbles, and 2 blue
marbles in the jar
∴ The total number of the marbles in the jar = 3 + 5 + 2 = 10
∵ Two marbles are drawn from the bag, one after the other without
replacement
- That means red is already occurred when green is happened,
so it is a "Conditional Probability" of green given red
P(B/A) = P(A and B)/P(A)
∵ Event A is defined as drawing a red marble from the jar on
the first draw
∴ P(A) = P(red)
∵ P(red) = [tex]\frac{3}{10}[/tex]
∴ P(A) = [tex]\frac{3}{10}[/tex]
∵ Event B is defined as drawing a green marble on the second draw
∴ P(B) = P(green)
- The number of marbles after the red is chosen is 9
∵ P(green) = [tex]\frac{5}{9}[/tex]
∴ P(B) = [tex]\frac{5}{9}[/tex]
- Find P( A and B)
∴ P(A and B) = ( [tex]\frac{3}{10}[/tex] ) . ( [tex]\frac{5}{9}[/tex] )
∴ P(A and B) = [tex]\frac{15}{90}[/tex]
- Simplify the fraction by divide up and down by 15
∴ P(A and B) = [tex]\frac{1}{6}[/tex]
∵ P(B|A) = P(A and B)/P(A)
- Substitute the values of P(A and B) and P(A) in the rule above
∴ P(B/A) = [tex]\frac{\frac{1}{6}}{\frac{3}{10}}[/tex]
- Simplify the fraction
∵ [tex]\frac{1}{6}[/tex] ÷ [tex]\frac{3}{10}[/tex] = [tex]\frac{1}{6}[/tex] × [tex]\frac{10}{3}[/tex] = [tex]\frac{10}{18}[/tex]
- Divide up and down by 2
∴ P(B/A) = [tex]\frac{5}{9}[/tex]
P(B/A) is [tex]\frac{5}{9}[/tex] in the simplest form
Learn more:
You can learn more about probability in brainly.com/question/10744457
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