Question

2)L : study was reported in whic h ninth grade Minnesota teens were asked whether they had gambles at least once a week in the past year. The sample consisted of 49.1% boys and 50.9% girls. The proportion of boys who had gambled at least once per week during the past year was 0.045. Let B the event the person is a boy, and C the event the person is a weekly gambler. a) Write each of the figures above in proper notation 0.229, while among girls this proportion was only b) Create a hypothetical two-way table to represent this situation c) Create a tree diagram to represent this situation. 09人10 0 1000

d) Find P(B and C) and write out what that outcome would represent. e) Find P(B]C) and write out what that outcome would represent.

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Answer #1

(a)

P(B) = 0.491. P(Β) = 0.509. P(CB) = 0.229. P(ClB) = 0.045

(b)

From above we have

Pl B n C) = P(CBP(B) = 0.229 . 0.491 0.11 2439

PlBN C) = P(Cl 3°)P(B) = 0.045 . 0.509 = 0.022905

By the complement rule we have

PlCB) 1-P(CB) = 1-0.229 = 0.771

P(с|B) = 1-P(CB) = 1-0.045 = 0.955

Now,

P(Β C*) = P(с|B) P(B) = 0.955 . 0.509 0.486095

PlBnC) = P(сBP(B) = 0.771 . 0.491 = 0.378561

b)

Total number of subjects 1000000.

Following is the completed two by two table:

Gambled No Total Yes (C) Boy (B) 0.112439*1000000-112439 0.378561*1000000 -378561 491000 Girl 0.022905 1000000 22905 0.486095 1000000-486095 509000 1000000 Total 135344 864656

c)

229 0.491 Ce BC 0.509 0.045 0.955 Ce

d)

Pl B n C) = P(CBP(B) = 0.229 . 0.491 0.11 2439

e)

From table we have

P(C)-804656- 0.864656

So,

. P(Bc กั CC) 0.486095 Pl BIC) = = 0.562183 P(C) _ 0.864656 -0.562183

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  • 2) A study was reported in which ninth grade Minnesota teens were asked whether they had...

    2) A study was reported in which ninth grade Minnesota teens were asked whether they had gambles at least once a week in the past year. The sample consisted of 49.1% boys and 50.9% girls. The proportion of boys who had gambled at least once per week during the past year was 0.229, while among girls this proportion was only 0.045. Let B the event the person is a boy, and C the event the person is a weekly gambler....

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