Question

1. Of the light bulbs available at a store, 42% are fluorescent, 23% are labeled as long life, and 12% are fluorescent and long life.

a. A light bulb will be selected at random from the light bulbs at this store. Rounding your answer to the nearest thousandth where necessary, find the probability that
i. The selected light bulb is not fluorescent.
ii. The selected light bulb is fluorescent given that it is labeled as long life.
b. Are the events "fluorescent" and "long life" independent? Explain.

Answer 1

Explanation:

Given

42% bulbs are fluorescent

23 % bulbs are long life

12% bulbs are fluorescent and long life

(i)Selected Bulb is not Fluorescent
`=1-P(bulb\ i\ fluorescent)`

`=1-0.42=0.58`

(ii)Selected light bulb is fluorescent given that it is labelled as long life

`P(Fluorescent\ given\ it\ long\ life)=(P(fluorescent\ and\ long\ life))/(P(long\ life))`

`P(Fluorescent\ given\ it\ long\ life)=(0.12)/(0.23)=0.52`

b.Fluorescent and long life events are not independent because if a bulb is fluorescent then it may be long life