Question

Numbered disks are placed in a box and one disk is selected at random. If there are 6 red disks numbered 1 through 6, and 2 yellow disks numbered 7 through 8, find the probability of selecting a red disk, given that an odd-numbered disk is selected.

Answer 1

`(3)/(4)`

Explanation:

Total number of red disk=6

Total number of yellow disk=2

Total disk=6+2=8

Odd number=1,3,5,7=4

Odd number on red disk=1,3,5=3

Probability,
`P(E)=(favorable\;cases)/(total\;number\;of\;cases)`

Using the formula

The probability of getting odd number disk=
`(4)/(8)=(1)/(2)`

The probability of getting odd numbered red disk=
`(3)/(8)`

The probability of selecting a red disk,given that an odd numbered disk is selected=
`((3)/(8))/((1)/(2))=(3)/(8)* 2=(3)/(4)`

Using conditional probability

`P(A/B)=(P(A\cap B))/(P(B))`