To find the experimental probability of at least 2 out of 5 flights arriving late, we need to count the number of times the digits 7, 8, or 9 appear in each group of 5 digits, and see how many of those groups have 2 or more of those digits. We can organize our counts in a table like this:
| | Flights | with | Late | Arrivals | |
|---|--------|-----|---------|-------------|
| | Digit | 7 | Digit | 8 | Digit | 9 | Total |
| 1 | 0 | 0 | 0 | 0 | 1 | 1 |
| 2 | 2 | 0 | 0 | 0 | 3 | 3 |
| 3 | 0 | 1 | 1 | 1 | 0 | 3 |
| 4 | 0 | 0 | 1 | 2 | 1 | 4 |
| 5 | 0 | 0 | 0 | 2 | 3 | 5 |
| 6 | 0 | 0 | 2 | 1 | 2 | 5 |
| 7 | 0 | 1 | 0 | 2 | 2 | 5 |
| 8 | 0 | 0 | 2 | 0 | 3 | 5 |
| 9 | 0 | 2 | 0 | 1 | 2 | 5 |
| 10 | 0 | 1 | 1 | 0 | 3 | 5 |
| 11 | 1 | 0 | 1 | 0 | 3 | 4 |
| 12 | 1 | 0 | 0 | 2 | 2 | 5 |
| 13 | 0 | 0 | 3 | 0 | 2 | 5 |
| 14 | 1 | 1 | 0 | 1 | 2 | 4 |
| 15 | 1 | 0 | 0 | 3 | 1 | 4 |
| Total | 5 | 6 | 11 | 15 | 28 | 60 |
For example, in row 2, we see that there are 3 groups of 5 digits where there are at least 2 late arrivals (digits 7, 8, or 9). To find the experimental probability, we need to add up the total number of groups that meet the criterion (at least 2 late arrivals) and divide by the total number of groups:
Experimental probability = (number of groups with at least 2 late arrivals) / (total number of groups)
Experimental probability = (11 + 15 + 28) / 60
Experimental probability = 54/60
Experimental probability = 9/10
Therefore, the answer is (C) start fraction 9 over 20 end fraction.
Suppose 10% of the flights arriving at an airport arrive early, 60% arrive on time, and 30% arrive late. Valerie used the random-number table to find the experimental probability that of 5 flights, at least 2 will arrive late. The digit 0 represents flights arriving early. The digits 1, 2, 3, 4, 5, and 6 represent flights arriving on time. The digits 7, 8, and 9 represent flights arriving late.
A table is shown with 4 rows and 5 columns.
• First Row First column 6 5 9 2 6 Second column 3 1 4 5 9 Third column 3 1 9 8 6 Fourth column 6 5 8 0 9 Fifth column 8 0 4 6 2
• Second Row First column 2 7 3 8 7 Second column 3 9 0 7 5 Third column 4 6 7 3 8 Fourth column 2 1 9 8 6 Fifth column 5 9 8 3 7
• Third Row First column 9 1 3 8 4 Second column 1 0 9 8 7 Third column 2 6 4 9 1 Fourth column 6 8 4 9 8 Fifth column 9 8 7 9 6
• Fourth Row First column 3 2 5 9 6 Second column 2 6 4 4 8 Third column 3 1 2 3 5 Fourth column 6 3 2 5 6 Fifth column 5 3 1 2 1
Find the experimental probability that of 5 flights, at least 2 will arrive late.
A. start fraction 3 over 10 end fraction
B. two-fifths
C. start fraction 9 over 20 end fraction
D. Start Fraction 11 over 20 End Fraction.
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