4 Points
2 answers:
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Answer:
a)
b)
Step-by-step explanation:
Conditional probability is the probability of one event occurring with some relationship to one or more other events.
The total probability rule (or the Law of Total Probability) breaks up probability calculations into distinct parts. P(AUB)=P(A)+P(B)-P(A and B)
The general multiplication rule formula is: P(A ∩ B) = P(A) P(B|A)=P(B)P(A|B)
We have the following probabilities:
Part a
We can use this multiplication rule:
For this part we want this probability:
And if we replace we got:
Part b
For this part we want the probability of one event in last year OR one event on the current year, so we can use the probability addition of events:
And for our case we have:
Answer:
a) 297°
b) 4.52 minutes
Step-by-step explanation:
a) Consider the attached figure. The boat's actual path will be the sum of its heading vector BA and that of the current, vector AC. The angle of BA north of west has a sine equal to 5/11. That is, the heading direction measured clockwise from north is ...
270° + arcsin(5/11) = 297°
__
b) The "speed made good" is the boat's speed multiplied by the cosine of the angle between the boat's heading and the boat's actual path. That same value can be computed as the remaining leg of the right triangle with hypotenuse 11 and leg 5.
boat speed = √(11² -5²) = √96 ≈ 9.7980 . . . . miles per hour
Then the travel time will be ...
time = distance/speed
(3900 ft)×(1 mi)/(5280 ft)×(60 min)/(1 h)/(9.7980 mi/h) ≈ 4.523 min
