Answer to Question #99096 in Statistics and Probability for Nayum uddin

Question

Suppose that one box contains 60 long bolts and 40 short bolts ,and that the other box contains 10 long bolts and 20 short bolts. Suppose also that one box is selected at random and a bolt is then selected at random from that box. Find the probability that
this bolt is long.

Answer 1

The probability that bolt is long when one select the.first box is 60/(60+40)=60/100=3/5 as the ratio of favorable events to the total number of events. For the second box this probability is 10/(10+20)=1/3. Probability to select the first box is 1/2, and probability to select the second box is 1/2 too. We are satisfied with both outcomes (the probabilities add up) if only the long bolt will be chosen.

P(long bolt)=(1/2)*(3/5)+(1/2)*(1/3)=3/10+1/6=(9+5)/30=14/30=7/15.

Answer:The probability that bolt will long is 7/15.