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of yarn purchased at a fiber festival and the probability that all of them will

ID: 3072569 • Letter: O

Question

of yarn purchased at a fiber festival and the probability that all of them will be used in craft projects in the # of skeins bought # of people who bought that many Probability of using them all (5) The following table gives us the relationship between the number of skeins next year 300 450 570 680 .90 .80 .65 .40 (a) What is the probability that if someone uses all their skeins of yarn, that person bought 3 skeins? (b) Suppose two friends shop together. If the number of skeins each buys is independent of the other's purchases, what is the probability that they will fall into the same category in this table?

Explanation / Answer

a)otal number of Skeins =300+450+570+680 =2000

here P(using all skeins)=P(1 skeins bought and use all)+P(2 skeins bought and use all)+P(3 skeins bought and use all)+P(4 skeins bought and use all)

=(300/2000)*0.9+(450/2000)*0.8+(570/2000)*0.65+(680/2000)*0.4=0.6363

hence P(buying 3 skeins given uses all of them)

=P(3 skeins bought and use all)/P(uses them all)=(570/2000)*0.65/0.6363 =0.2911

b)

P(fall into same category)=P(first and second both bought 1 skeins)+P(first and second both bought 2 skeins)+P(first and second both bought 3 skeins)+P(first and second both bought 4+ skeins)

=(300/2000)*(300/2000)+(450/2000)*(450/2000)+(570/2000)*(570/2000)+(680/2000)*(680/2000)

=0.27