Question

The probability P of choosing an object at random from a group of objects is found by the fraction P(event) = Number of favorable outcomes Total number of outcomes . Suppose the angle measures 30°, 60°, 120°, 150° are written on slips of paper. You choose two slips of paper at random. What is the probability that the measures you choose are complementary? The probability of choosing complementary measures is

Answer 1

Answer:

P(c)  = 0,0833     or      P(c)  =  8.33 %

Step-by-step explanation:

Comlementary angles a thse which sum s 90⁰. xamles of complementay angles ae:

75⁰ and 15⁰

80⁰ and 10⁰

5⁰  and 85⁰

and s forth

From the group of given angles:

30⁰ ,  60⁰,  120⁰ , 150⁰

only the couple   30⁰ ,  60⁰ meet the request, that means are complementary (the sum is 90⁰).

So we only have one chance of chossing such a couple. The number of favorable outcomes is 1 )

Now we have 4 slips of paper (that means 4 elements, and the quantity of different pairs we can get combining these 4 elements is given by the combination of four (4) elements in group of two. That is:

C₄,₂  =  4! /  ( 4 - 2 )!     ⇒   C₄,₂  = 4*3*2*1 / 2*1    ⇒  C₄,₂  = 4*3  

C₄,₂  = 12  (Total number of outcomes)

Then the probability of chossing two slips of paper that the measure are complementary is:

P(c)  =  1 / 12       ⇒  P(c)  = 0,0833       ⇒     P(c)  =  8.33 %