Can someone please help me with a couple questions?
1)The probability that a dessert sold at a certain cafe contains chocolate is 73%. The probability that a dessert containing chocolate also contains nuts is 25%. Find the probability that a dessert at random contains nuts given that it contains chocolate. Round to the nearest tenth of a percent.
2)An airline has 81% of its flights depart on schedule. It has 69% of its flights depart and arrive on schedule. Find the probablitiy that a flight that departs on schedule also arrives on schedule?
34.2 %
Sure, I can help you with that. Let's answer your questions step-by-step:
1) To find the probability that a dessert at random contains nuts given that it contains chocolate, we need to use conditional probability.
We are given:
- The probability that a dessert contains chocolate is 73% (or 0.73).
- The probability that a dessert containing chocolate also contains nuts is 25% (or 0.25).
To find the probability that a dessert contains nuts given that it contains chocolate, we'll use the formula for conditional probability:
P(Nuts | Chocolate) = P(Nuts and Chocolate) / P(Chocolate)
P(Nuts and Chocolate) represents the probability that a dessert contains both nuts and chocolate.
So we have:
P(Nuts | Chocolate) = P(Nuts and Chocolate) / P(Chocolate) = 0.25 / 0.73
Calculating this, we find:
P(Nuts | Chocolate) ≈ 0.3425
Therefore, the probability that a dessert at random contains nuts given that it contains chocolate is approximately 34.3%.
2) To find the probability that a flight that departs on schedule also arrives on schedule, we'll use conditional probability.
We are given:
- The probability that a flight departs on schedule is 81% (or 0.81).
- The probability that a flight departs and arrives on schedule is 69% (or 0.69).
To find the probability that a flight arrives on schedule given that it departs on schedule, we'll use the formula for conditional probability:
P(Arrives | Departs) = P(Arrives and Departs) / P(Departs)
P(Arrives and Departs) represents the probability that a flight both arrives and departs on schedule.
So we have:
P(Arrives | Departs) = P(Arrives and Departs) / P(Departs) = 0.69 / 0.81
Calculating this, we find:
P(Arrives | Departs) ≈ 0.8518
Therefore, the probability that a flight that departs on schedule also arrives on schedule is approximately 85.2%.
Of course! I can help you with those questions. To find the probability that a dessert contains nuts given that it contains chocolate (question 1), we can use the concept of conditional probabilities.
1) Probability of nuts given chocolate:
Let's assume the event of a dessert containing chocolate as "C" and the event of a dessert containing nuts as "N". We are given that the probability of C (P(C)) is 73% and the probability of N given C (P(N|C)) is 25%. We want to find the probability of N given C (P(N|C)).
The formula for conditional probability is: P(N|C) = P(N∩C) / P(C)
Here, P(N∩C) represents the probability of both N and C occurring together.
To find P(N∩C), we can multiply the probability of C (P(C)) by the probability of N given C (P(N|C)).
P(N∩C) = P(C) * P(N|C)
P(N∩C) = 0.73 * 0.25 = 0.1825
Now, we can substitute the values we found into the formula for conditional probability:
P(N|C) = P(N∩C) / P(C) = 0.1825 / 0.73
P(N|C) ≈ 0.25 (rounded to the nearest tenth of a percent)
Therefore, the probability that a dessert at random contains nuts given that it contains chocolate is approximately 25%.
2) Probability of arrival on schedule given departure on schedule:
Let's assume the event of a flight departing on schedule as "D" and the event of a flight arriving on schedule as "A". We are given that the probability of D (P(D)) is 81% and the probability of both D and A occurring together (P(A∩D)) is 69%. We want to find the probability of A given D (P(A|D)).
Using the same formula for conditional probability, we can substitute the values into the formula:
P(A|D) = P(A∩D) / P(D)
We already have the values for P(A∩D) and P(D), so we can substitute them:
P(A|D) = 0.69 / 0.81 ≈ 0.852 (rounded to the nearest tenth of a percent)
Therefore, the probability that a flight departs on schedule and arrives on schedule is approximately 85.2%.