Expected Trials in Random Sampling
A teacher is selecting a sample of 10 students from 80 by reading two-digit numbers from a random digit table. Each two-digit number has an 80% chance (i.e., probability $$0.80$$) of being valid. What is the expected number of two-digit pairs the teacher must read to obtain 10 valid, unique numbers?
Random Digit Table Sample:
| 12 | 85 | 47 | 33 |
| 76 | 09 | 81 | 50 |
Note: Sequences like 85 and 81 would be skipped since they exceed 80.
A
$$8$$
B
$$12.5$$
C
$$15$$
D
$$10$$
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