Question

-g The side measurement of a plastic die, manufactured by factory A, is a random number between 1 and 1 1 4 centimeters. What is the probability that the volume of a randomly selected die manufactured by this company is greater than 1.424

Answer 1

Probability that the volume of a randomly selected die is greater than 1.424 will be 0.1194

Explanation:

The side measurement of the plastic die is a random number between 1 and 1.14 cm.

Therefore, minimum volume of the die (with one side 1 cm)
`V_(min.)` = 1 cm³

Maximum volume of the die (with one side 1.14 cm)
`V_(max.)` = (1.14)³ cm³

= 1.4815 cm³

Probability that the volume of a randomly selected die is greater than 1.424 cm³ =
`\frac{(V_{\text{max}}-1.424)}{(V_{\text{max}-V_{\text{min}}})}`

=
`((1.4815-1.424))/((1.4815-1))`

=
`(0.0575)/(0.4815)`

= 0.1194

Therefore, probability that the volume of a randomly selected die is greater than 1.424 will be 0.1194