To determine if being a kid and preferring hot dogs are independent, we need to calculate the probabilities and see if the probability of both events happening together is equal to the product of the probabilities of the two individual events.
Total number of kids = 8 (hamburger kids) + 12 (hot dog kids) = 20
Total number of adults = 17 (hamburger adults) +13 (hot dog adults) = 30
Total number of people = 20 (kids) + 30 (adults) = 50
Probability of being a kid (P(A)) = Total kids / Total people = 20 / 50 = 0.4
Probability of preferring hot dogs (P(B)) = Total hot dog preferences / Total people = 25 / 50 = 0.5
Probability of both being a kid and preferring hot dogs (P(A ⋂ B)) = Hotdog kids / Total people = 12 / 50 = 0.24
Now, if being a kid (A) and preferring hot dogs (B) are independent, then P(A ⋂ B) = P(A) * P(B).
Let's check if this holds true:
P(A) * P(B) = 0.4 * 0.5 = 0.2
Since P(A ⋂ B) ≠ P(A) * P(B) (0.24 ≠ 0.2), being a kid and preferring hot dogs are NOT independent events.
50 kids and adults are surveyed about weather for hamburgers or hotdogs the results are shown in the table the table.
kids adults
hamburgers 8. 17
hot dogs. 12. 13
are being a kid and preferring hotdogs independent? explain how you know
1 answer