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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 colourP(H)P(S)
Red0.50.8
Blue0.40.5
Green0.10.5
Advika is spotted outdoors wearing both a Hat and Sunglasses. What is the probability that she is wearing the Red scarf?

  1. A \(\dfrac{4}{9}\)
  2. B \(\dfrac{13}{313}\)
  3. C \(\dfrac{8}{13}\)
  4. D \(\dfrac{8}{21}\)
Verified Solution

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…