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. Find the experimental probability that of 5 flights, at least 2 will arrive late.
This is an experimental probability project.
Ideally you will need a 10-sided die (can get from toy/game stores) in the shape of a duodecahedron (10 identical faces), and proceed as described.
The more trials you make, the closer it should approach the expected values, i.e. 10% early, 60% on time and 30% late.
Your results should include the number of trials and the results obtained.
I would start with 3-4 experiments with 10 trials, about 1 or 2 with 100 trials.
If you are familiar with random number tables or programming, you can do it on the computer as well.
Thanks for explaining
To find the experimental probability that of 5 flights, at least 2 will arrive late, we need to consider the different combinations of flights that meet this condition.
First, let's find the probability of having exactly 2 flights arriving late:
P(2 flights arriving late) = (0.3)^2 * (0.7)^3
Next, let's find the probability of having exactly 3 flights arriving late:
P(3 flights arriving late) = (0.3)^3 * (0.7)^2
Finally, let's find the probability of having exactly 4 or 5 flights arriving late, which includes having all 5 flights arriving late:
P(4 or 5 flights arriving late) = (0.3)^4 * (0.7)^1 + (0.3)^5
To find the total experimental probability, we sum up the probabilities of each case:
Experimental probability = P(2 flights arriving late) + P(3 flights arriving late) + P(4 or 5 flights arriving late)
Experimental probability = (0.3)^2 * (0.7)^3 + (0.3)^3 * (0.7)^2 + (0.3)^4 * (0.7)^1 + (0.3)^5
Now we can calculate the experimental probability using the above formula.
To find the experimental probability that at least 2 out of 5 flights will arrive late, we need to determine the possible outcomes and count the favorable outcomes.
First, let's consider the possible outcomes for each flight: early arrival (E), on-time arrival (O), and late arrival (L).
Based on the information given, the probability of E is 10%, O is 60%, and L is 30%.
Now, let's count the favorable outcomes for at least 2 out of 5 flights arriving late.
To do this, we can make use of the digit representations given in the question:
- 0 represents E (early arrival)
- 1, 2, 3, 4, 5, and 6 represent O (on-time arrival)
- 7, 8, and 9 represent L (late arrival)
Since we want to find the probability of at least 2 L's, we need to consider the following possibilities:
1. Exactly 2 flights arriving late: LLxxx (80% * 80% * 20% * 20% * 80% = 0.128). Here, "x" represents any arrival (E or O).
To calculate the probability, we multiply the chances of L, L, E/O, E/O, and E/O.
2. Exactly 3 flights arriving late: LLLxx (80% * 80% * 80% * 20% * 20% = 0.1024).
3. Exactly 4 flights arriving late: LLLLx (80% * 80% * 80% * 80% * 20% = 0.065536).
4. All 5 flights arriving late: LLLLL (80% * 80% * 80% * 80% * 80% = 0.32768).
To find the experimental probability, we sum up the probabilities of all these favorable outcomes:
P(at least 2 flights arriving late) = (0.128 + 0.1024 + 0.065536 + 0.32768) = 0.623736.
Therefore, the experimental probability that of 5 flights, at least 2 will arrive late is approximately 0.623736, or about 62.37%.