Question

A box contains 5 red, 8 blue and 3 green pens.
Rutuja wants to pick a pen at random.What is the probability that the pen is blue?

Answer 1

Here, there are 5 red pens `R_(1),R_(2),R_(3),R_(4),R_(5).`
8 blue pens `B_(1),B_(2),B_(3),B_(4),B_(5),B_(6),B_(7),B_(8).`
3 green pens `G_(1),G_(2),G_(3).`
`therefore "the sample space"`
`S={R_(1),R_(2),R_(3),R_(4),R_(5),B_(1),B_(2),B_(3),B_(4),B_(5),B_(6),B_(7),B_(8),G_(1),G_(2),G_(3)}`
`n(S)=16`
Let A be the event that Rutuja picks a blue pen.
`Then A={B_(1),B_(2),B_(3),B_(4),B_(5),B_(6),B_(7),B_(8)}`
`thereforen(A)=8`
`P(A)=(n(A))/(n(S))=(8)/(16)=(1)/(2)`
`therefore"the probability that Rutuja picks a blue pen is" (1)/(2)`