<p>Three faces of a fair dice are yellow, two are red and one is blue. Find the probability that the dice shows <strong>(a)</strong> yellow, <strong>(b)</strong> red and <strong>(c)</strong> blue face.</p>
Step-by-Step Solution
Key Concept: Probability is the ratio of favorable outcomes to total possible outcomes. Since the die has 6 faces with specified colors, count the faces of each color and divide by 6.
<p><strong>Step 1:</strong> Identify the composition of the die.</p><p>Yellow faces = 3, Red faces = 2, Blue faces = 1, Total faces = 6</p><p><strong>Step 2:</strong> Apply the classical probability formula: P(Event) = (Number of favorable outcomes)/(Total possible outcomes)</p><p><strong>Step 3:</strong> Calculate each probability.</p><p>(a) P(Yellow) = 3/6 = <strong>1/2</strong></p><p>(b) P(Red) = 2/6 = <strong>1/3</strong></p><p>(c) P(Blue) = 1/6 = <strong>1/6</strong></p><p><strong>Verification:</strong> 1/2 + 1/3 + 1/6 = 3/6 + 2/6 + 1/6 = 6/6 = 1 ✓</p><p>∴ Answer: (a) 1/2, (b) 1/3, (c) 1/6</p>
Correct Answer: (a) \(\dfrac{1}{2}\), (b) \(\dfrac{1}{3}\), (c) \(\dfrac{1}{6}\)