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There are 4 yellow marbles, 6 green marbles, and 5 blue marbles in a jar. Event A is defined as drawing a green marble from the jar on the first draw. Event B is defined as drawing a yellow marble on the second draw.
If two marbles are drawn from the bag, one after the other without replacement, what is P(B|A) expressed in simplest form?

A)4/15
B)2/7
C)1/3
D)2/5

Respuesta :

Answer:(a)

Step-by-step explanation:

Given

There are 4 yellow, 6 green and 5 blue marbles

We have to find [tex]P(B\mid A)[/tex] i.e. conditional probability of B given that A is occurred.

[tex]P(B\mid A)[/tex] is given by

[tex]P(B\mid A)=\dfrac{P(A\cap B)}{P(A)}[/tex]

Also A=drawing a green marble

B=drawing a yellow marble

Total no of marbles [tex]=4+6+5=15[/tex]

So,

[tex]P(A)=\dfrac{6}{15}[/tex]

similarly [tex]P(B)=\dfrac{4}{15}[/tex]

[tex]P(A\cap B)=P(A)\times P(B)[/tex]

[tex]P(A\cap B)=\dfrac{6}{15}\times \dfrac{4}{15}[/tex]

[tex]P(A\cap B)=\frac{24}{225}[/tex]

Substituting the values in the formula

[tex]P(B\mid A)=\dfrac{\frac{24}{225}}{\frac{6}{15}}[/tex]

[tex]P(B\mid A)=\frac{24}{6}\times \frac{15}{225}[/tex]

[tex]P(B\mid A)=\frac{4}{15}[/tex]

elliejohnson1002

Answer:

its acttually B

Step-by-step explanation:

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