supposed 10% of the flights arriving I didn’t airport or Everly 60% arrive on time and 30% Rivelly. Valerie used a random number table to find the excremental probability that five of the fights at least to arrive. We did the dishes zero represents play it’s Robin early digits 123456 represent flights arriving on time for digit 789 represents flights, arriving late I’m extramental probability that five flights at least 2 will arrive late
To find the extramental probability that at least 5 flights arrive, we can use the binomial distribution formula:
P(X ≥ 5) = 1 - P(X < 5)
where X is the number of flights that arrive on time out of 10 flights.
The probability that a flight arrives on time is 0.6, and the probability that a flight arrives late is 0.3.
Using the binomial distribution formula and the complement rule, we have:
P(X < 5) = ΣP(X = x) for x = 0 to 4
= C(10,0)(0.6)^0(0.4)^10 + C(10,1)(0.6)^1(0.4)^9 + C(10,2)(0.6)^2(0.4)^8 + C(10,3)(0.6)^3(0.4)^7 + C(10,4)(0.6)^4(0.4)^6
= 0.000105
Therefore,
P(X ≥ 5) = 1 - P(X < 5)
= 1 - 0.000105
= 0.999895
This means that the extramental probability that at least 5 flights arrive is 0.999895.
To find the extramental probability that at least 2 flights arrive late, we can use a similar approach:
P(Y ≥ 2) = 1 - P(Y < 2)
where Y is the number of flights that arrive late out of 10 flights.
Using the complement rule and the binomial distribution formula, we have:
P(Y < 2) = ΣP(Y = y) for y = 0 to 1
= C(10,0)(0.3)^0(0.7)^10 + C(10,1)(0.3)^1(0.7)^9
= 0.0282485
Therefore,
P(Y ≥ 2) = 1 - P(Y < 2)
= 1 - 0.0282485
= 0.9717515
This means that the extramental probability that at least 2 flights arrive late is 0.9717515.
To find the experimental probability that five flights will arrive at least two flights arriving late, we need to analyze the given information.
According to the information provided:
- 10% of flights arriving late: This means 10% of flights will have a digit 7, 8, or 9 in the random number table.
- 60% of flights arriving on time: This means 60% of flights will have a digit 1, 2, 3, 4, 5, or 6 in the random number table.
- 30% of flights arriving early: This means 30% of flights will have a digit 0 in the random number table.
Since Valerie wants to find the probability that five flights will have at least two flights arriving late, we need to consider different scenarios.
1. Five flights arrive, and exactly two of them are late:
We select two random numbers from the digits 7, 8, and 9 (arriving late) and three random numbers from digits 1 to 6 (arriving on time).
The probability of selecting two digits from 7, 8, and 9 is:
(3/10) * (3/10) = 9/100
The probability of selecting three digits from 1 to 6 is:
(6/10) * (6/10) * (6/10) = 216/1000 = 54/250
The combined probability for this scenario is:
(9/100) * (54/250) = 486/25000
2. Five flights arrive, and exactly three of them are late:
We select three random numbers from the digits 7, 8, and 9 (arriving late) and two random numbers from digits 1 to 6 (arriving on time).
The probability of selecting three digits from 7, 8, and 9 is:
(3/10) * (3/10) * (3/10) = 27/1000
The probability of selecting two digits from 1 to 6 is:
(6/10) * (6/10) = 36/100
The combined probability for this scenario is:
(27/1000) * (36/100) = 972/100000
3. Five flights arrive, and exactly four of them are late:
We select four random numbers from the digits 7, 8, and 9 (arriving late) and one random number from digits 1 to 6 (arriving on time).
The probability of selecting four digits from 7, 8, and 9 is:
(3/10) * (3/10) * (3/10) * (3/10) = 81/10000
The probability of selecting one digit from 1 to 6 is:
(6/10) = 6/10
The combined probability for this scenario is:
(81/10000) * (6/10) = 486/100000
4. Five flights arrive, and all of them are late:
We select five random numbers from the digits 7, 8, and 9 (arriving late).
The probability of selecting five digits from 7, 8, and 9 is:
(3/10) * (3/10) * (3/10) * (3/10) * (3/10) = 243/100000
To find the probability that at least two flights will arrive late, we add up the probabilities for each scenario we calculated above:
(486/25000) + (972/100000) + (486/100000) + (243/100000) = 1187/10000
Therefore, the experimental probability that five flights will have at least two flights arriving late is 1187/10000.
To find the excremental probability that at least two out of five flights will arrive late, we need to calculate the probability of different scenarios where two or more flights arrive late.
We are given that 10% of flights arrive late, and we can use this information to determine the probability of a flight arriving late. From the given data, we know that 60% of the flights arrive on time, and 30% arrive late.
To calculate the probability of each scenario, we need to use the concept of "combination." The formula for combination is:
C(n, r) = n! / (r!(n-r)!)
Where n is the total number of possible events, and r is the number of events we are interested in.
Scenario 1: Exactly two flights arrive late
In this case, we need to select two flights out of five that will arrive late. The probability of one flight arriving late is 30%, so the probability of two flights arriving late is (0.3)^2.
The probability for this scenario is: C(5, 2) * (0.3)^2 * (0.7)^3
Scenario 2: Exactly three flights arrive late
Similarly, we calculate the probability of selecting three flights out of five that will arrive late. The probability of one flight arriving late is 30%, so the probability of three flights arriving late is (0.3)^3.
The probability for this scenario is: C(5, 3) * (0.3)^3 * (0.7)^2
Scenario 3: Exactly four flights arrive late
Following the same logic, the probability for this scenario is: C(5, 4) * (0.3)^4 * (0.7)^1
Scenario 4: All five flights arrive late
Again, using the probability of 30% for each flight being late, the probability for this scenario is: C(5, 5) * (0.3)^5 * (0.7)^0
To find the excremental probability that at least two flights will arrive late, we need to add up the probabilities of these four scenarios:
Excremental Probability = Probability of Scenario 1 + Probability of Scenario 2 + Probability of Scenario 3 + Probability of Scenario 4
Keep in mind that you mentioned using a random number table to find the excremental probability. In this case, you would need to use the table to generate random numbers between 1 and 9, representing the arrival times of the flights (1-6 for on time, 7-8 for late). By repeatedly generating random numbers and counting the occurrences of at least two late arrivals out of five flights, you can approximate the excremental probability.