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Sagot :
Answer:
See below ~
Step-by-step explanation:
Probability Equation
- P (A ∪ B) = P (A) + P (B) - P (A ∩ B)
Let :
- P (wearing a scarf) = P (A)
- P (math quiz) = P (B)
Solving the equation
- 5% = 10% + 15% - P (A ∩ B)
- 5% = 25% - P (A ∩ B)
- P (A ∩ B) = 20%
For independent events, P (A ∩ B) = 0% = ∅
Therefore, they are not independent events.
Answer:
Let "wearing a scarf" = S
Let "math quiz" = Q
Given:
- P(S) = 10% = 0.1
- P(Q) = 15% = 0.15
- P(S ∩ Q) = 5% = 0.05
The product law for independent events A and B is:
P(A ∩ B) = P(A)P(B)
Therefore, to determine if events S and Q are independent:
⇒ P(S)P(Q) = 0.1 × 0.15 = 0.015 = 1.5%
Therefore, as 1.5% ≠ 5% the events are not independent.
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