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.
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.
To find the experimental probability that at least 2 flights will arrive late, we need to analyze the random-number table.
Looking at the table, we can count the number of times we see digits 7, 8, or 9 in each column for each row.
Counting the number of 7, 8, or 9s in each column, we have:
Column 1: 5 (from the first and fourth columns of the second row)
Column 2: 6 (from the second and fifth columns of the second row)
Column 3: 6 (from the third and fourth columns of the second row)
Column 4: 9 (from the second, third, fourth, and fifth columns of the first row)
Column 5: 7 (from the second, third, fourth, and fifth columns of the first row)
Now we need to sum up the counts to determine the total number of flights that arrive late:
Total number of flights arriving late = 5 + 6 + 6 + 9 + 7 = 33
Next, we need to calculate the experimental probability by dividing the number of favorable outcomes (flights arriving late) by the total number of outcomes (total number of flights).
Total number of outcomes (total number of flights) = 5 flights per row x 4 rows = 20 flights
Experimental Probability of at least 2 flights arriving late = Total number of favorable outcomes / Total number of outcomes
= 33 / 20
Simplifying the fraction, we get:
Experimental Probability of at least 2 flights arriving late = 1.65
However, experimental probabilities are usually expressed as fractions or ratios. Therefore, the correct answer choice is not listed.