A group of 84 were randonmly selected and asked to draw the correct size of a ni

Question

A group of 84 were randonmly selected and asked to draw the correct size of a nickel. Each child's income group was recorded and and some children drew the nickel too large a diameter and some drew it with too small of a diameter. The results are summarized in the table below Too Small Too Large Total 36 48 42 84 16 26 Low Income 20 High Income Total 42 For accuracy purposes give your answers as fractions or as a calculation involving fractions. No decimal entries If one child from the group is selected, find the following probabilities. (a) The child is from the low income group (b) The child is from the high income group and drew the nickel too large (e) The child drew the nickel too small given that the child was from the low income group (d) The child is from the high income group or drew the nickel too large Preview Preview Preview Preview (e) Now, if two different children are randomly selected from this group, find the probability that both children drew the nickel too large Preview

Explanation / Answer

a) P(from the low income group) = 36/84 = 9/21

b) P(high income group and nickle too large) = 26/84 = 13/42

c) P(nickle too small | low income group) = P(nickle too small and low income group)/P(low income group)

                                                                  = 20/36 = 5/9

d) P(high income group or nickle too large) = P(high income group) + P(nickle too large) - P(high income group and nickle too large)

                                                                     = 48/84 + 42/84 - 26/84 = (48 + 42 - 26)/84 = 64/84 = 16/21

e) P(both children drew the nickle too large) = 42C2/84C2 = 861/3486 = 123/498

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