Please hurry!!!! G SAMPLE SPACES JUSTIFY YOUR ANSWERS for 18 points) An urn cont

Question

Please hurry!!!!

G SAMPLE SPACES JUSTIFY YOUR ANSWERS for 18 points) An urn contains five balls numbered 1,2,3,4, and 5 FULL CREDIT ely. Assume a random experiment for this experimen two balls without numeric values. replacement from the urn and writing down the sum of the two struct a sample space for this experiment in which each of the outcomes as equal likelihood. (a) Constru ct a sam (b) Find the probability that the sum of the numeric values is equal to 5. (c) Find the probability that the sum of the numeric values is six given that the sum of the numeric values is even.

Explanation / Answer

a)

The possible sums are 3, 4, 5, 6, 7, 8, 9

So, Sample space: {3, 4, 5, 6, 7, 8, 9}

The possible pairs are (1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5) which are 10 in number.

b)

The sum of 5 can be obtained when the outcomes are (1,4) or (2,3)

So, P(sum of numeric values is equal to 5) = 2/10 = 0.20

c)

P(sum of numeric values is 6 given that sum of numeric values is even) = P(sum of numeric values is 6 and that sum of numeric values is even) / P(sum of numeric values is even)

Sum of numeric values is 6 and that sum of numeric values is even --- This can occur when the outcomes are (1,5), (2,4).

So, P(sum of numeric values is 6 and that sum of numeric values is even) = 2/10 =0.20

Sum of numeric values is even--- This can occur when the outcomes are (1,3),(1,5),(2,4),(3,5)

So, P(sum of numeric values is even) = 4/10 =0.40

Thus, P(sum of numeric values is 6 given that sum of numeric values is even) = 0.20 / 0.40 = 0.50

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