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) = $\frac{3}{10}$

∴ P(A) = $\frac{3}{10}$

∵ 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) = $\frac{5}{9}$

∴ P(B) = $\frac{5}{9}$

- Find P( A and B)

∴ P(A and B) = ( $\frac{3}{10}$ ) . ( $\frac{5}{9}$ )

∴ P(A and B) = $\frac{15}{90}$

- Simplify the fraction by divide up and down by 15

∴ P(A and B) = $\frac{1}{6}$

∵ 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) = $\frac{\frac{1}{6}}{\frac{3}{10}}$

- Simplify the fraction

∵ $\frac{1}{6}$ ÷ $\frac{3}{10}$ = $\frac{1}{6}$ × $\frac{10}{3}$ = $\frac{10}{18}$

- Divide up and down by 2

∴ P(B/A) = $\frac{5}{9}$

P(B/A) is $\frac{5}{9}$ in the simplest form

Learn more:

You can learn more about probability in brainly.com/question/10744457

#LearnwithBrainly

7 0

2 years ago