1000 sealed envelopes: 10 contain Rs 100, 100 contain Rs 50, 200 contain Rs 10, rest contain no cash. If one is picked at random, probability it contains no cash prize?
\(\dfrac{69}{100}\)
Step 1: Total number of envelopes = 1000.
Step 2: Count the envelopes that have money:
Step 3: Add them: \(10 + 100 + 200 = 310\).
Step 4: Envelopes with no cash = Total − With cash = \(1000 − 310 = 690\).
Step 5: Probability formula: \[ P(\text{event}) = \dfrac{\text{Favourable outcomes}}{\text{Total outcomes}} \] Here, favourable = 690, total = 1000.
Step 6: \( P = \dfrac{690}{1000} = \dfrac{69}{100} \).
Final Answer: Probability that it contains no cash = \(\dfrac{69}{100}\).