Question

The numbered disks shown are placed in a boxand one disk is selected at random. Find theprobability of selecting a 6, given that a blue diskis selected.Find the probability of selecting a 6, given that a blue disk is selected.(Type an integer or a simplified fraction.)

Answer 1

The probability of selecting a 6, given that a blue disk is selected is given by the following formula:

$P(B|A)=P(A\text{ n B\rparen/P\lparen A\rparen}$

There are 4 blue in : 1, 2 , 6, 8

P(A)= blue disk selected:

P(B)= 6 is selected

$P(A)=\frac{4}{8}=\frac{1}{2}.$

$P(A\text{ }n\text{ B})=P(A)*P(B)=\frac{1}{2}*\frac{1}{4}=\frac{1}{8}$

Where P(B) is the probablity to select the number 6 in four blue disks.

Substituing:

$\begin{gathered} P(A|B)=(\frac{1}{8})\text{ /\lparen1/2\rparen} \\ \\ P(A|B)=\frac{1}{4} \end{gathered}$

Answer: The probablity to select a 6, given that a blue disk was selected is: 1/4.