Consider two events such that P(A)=3/4, P(B)=2/5 and P(AnB)=1/3. Are the events A and B independent?

1 answer:

6 0

If P(A) times P(B) is equal to P(A n B), then that shows the events are independent. Otherwise, they are dependent. When I write "A n B", I mean "A intersect B". The intersect symbol looks similar to the lowercase letter n.

P(A)*P(B) = (3/4)*(2/5) = (3*2)/(4*5) = 6/20 = 3/10

Since that result is not the same as P(A n B) = 1/3, this means that the events are not independent. They are dependent events. The answer is choice D

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The sales tax rate in Wilson County is 6.75%. Suppose total price of an item that you bought in Wilson County including taxes i

schepotkina [342]

Sales Tax rate: 6.75%
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x+0.0675x = 14.93 -- we change the percent to decimal

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2 years ago

In triangle ABC, a = 3, b = 5, and c = 7. Find the approximate value of angle A.

OLEGan [10]

9514 1404 393

Answer:

a) 22°

Step-by-step explanation:

Side 'a' is the shortest side, so angle A will be the smallest angle. Its value must be less than 60°, eliminating the last two answer choices. The actual value can be found from the Law of Cosines.

a² = b² +c² -2bc·cos(A)

cos(A) = (b² +c² -a²)/(2bc) = (5² +7² -3²)/(2(5)(7)) = 65/70

A = arccos(65/70) ≈ 21.7868°

Angle A is about 22°.