COMEDK · Maths · 36. Probability
Advika chooses one of three scarves every morning: Red, Blue, or Green.
• The probability she chooses Red is 20%.
• The probability she chooses Blue is twice the probability of choosing Red.
• On the remaining days she wears a Green scarf.
Once a scarf is chosen, she decides whether to wear a Hat (H) and Sunglasses (S). These choices are independent of each other but depend on the scarf colour:
| Scarf colour | P(H) | P(S) |
|---|---|---|
| Red | 0.5 | 0.8 |
| Blue | 0.4 | 0.5 |
| Green | 0.1 | 0.5 |
- A \(\dfrac{4}{9}\)
- B \(\dfrac{13}{313}\)
- C \(\dfrac{8}{13}\)
- D \(\dfrac{8}{21}\)
Answer & Solution
Correct Answer
(A) \(\dfrac{4}{9}\)
Step-by-step Solution
Detailed explanation
Let \(R\), \(B\), and \(G\) be the events of choosing Red, Blue, and Green scarves respectively. \(P(R) = 0.2\) \(P(B) = 2 \times 0.2 = 0.4\) \(P(G) = 1 - (0.2 + 0.4) = 0.4\) Let \(E\) be the event of wearing both a Hat and Sunglasses. Since the choices are independent for a…
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