Question

There are 5 blue crayons, 7 yellow crayons, and 8 red crayons. in a box. If one is randomly drawn and replaced 15 times, find the probability of drawing exactly four blue crayons?

Answer 1

`0.2252`

Explanation:

`"There are 5+7+8 = 20 crayons in total."`
`=> P = C(15,4) (5/20)^4 (15/20)^11`
`= ((15!) 5^4 15^11) / ((11!)(4!) 20^15)`
`= 0.2252`

`"Explanation :"`
`"Because we replace, the odds for drawing a blue crayon are"`
`"each time 5/20. We express that we draw 4 times a blue one"`
`"and then 11 times not a blue one by (5/20)^4 (15/20)^11."`
`"Of course the blue ones do not have to be drawn first so there"`
`"are C(15,4) ways of drawing them, so we multiply by C(15,4)."`

`"and C(15,4) "= (15!)/(11!4!) " (combinations)"`