Question

A jam manufacturer knows that in a box of 48 jars,5 will contain less jam than shown on the label. Determine the probability that 2 jars drawn at random will contain less jam.

Answer 1

Probability that 2 jars drawn at random will contain less jam is 0.00886524822

Explanation:

A jam manufacturer knows that in a box of 48 jars,5 will contain less jam than shown on the label. Now we have to find the probability that 2 jars drawn at random will contain less jam.

Given 5 jars contain less jam as shown on label. So 2 jars drawn at random from these 5 jars therefore number of ways or favourable outcome will be
`_(2)^(5)\textrm{C}`

Total no. of outcomes=
`_(2)^(48)\textrm{C}`

P(2 jars with less jam)=
`(Favourable outcome)/(Total outcomes)`

=
`\frac{_(2)^(5)\textrm{C}}{_(2)^(48)\textrm{C}}`

=
`((5!)/(2!3!))/((48!)/(2!46!))=(5)/(12(47))=0.00886524822`

Hence, probability that 2 jars drawn at random will contain less jam is 0.00886524822