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

Answer:

$\frac{3}{4}$

Step-by-step 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,$P(E)=\frac{favorable\;cases}{total\;number\;of\;cases}$

Using the formula

The probability of getting odd number disk=$\frac{4}{8}=\frac{1}{2}$

The probability of getting odd numbered  red disk=$\frac{3}{8}$

The probability of selecting a red disk,given that an odd numbered disk is selected=$\frac{\frac{3}{8}}{\frac{1}{2}}=\frac{3}{8}\times 2=\frac{3}{4}$

Using conditional probability

$P(A/B)=\frac{P(A\cap B)}{P(B)}$