Each of the 12 cards shown has a number and a color or pattern. each card is equally likely to be drawn. find each probability.

check linked image ^^

A) P(stars) = 1/3

B) P(odd)= 4/7

C)P(solid grays or stars or striped)= 1

D)P(1,4 or 7)= 3/7

E)P(not striped)= 2/3

Step-by-step explanation:

Given:

sample set contains 1-7 solid gray, 1-7 stars and 1-7 striped cards

Let solid gray be x

stars be y

striped be z

then sample set be

1x,2x,3x,4x,5x,6x,7x,

1y,2y,3y,4y,5y,6y,7y,

1z,2z,3z,4z,5z,6z,7z

total number of cards in sample set =21

Now

a)Finding probability of stars

Number of star cards in above sample set = 7

P(stars)= 7/21

     P(y)=1/3

b)Finding probability of odd

Number of odd cards in above sample set = 12

P(odd)= 12/21

          =4/7

c)Finding probability of solid grays or stars or striped

P(solid grays or stars or striped) = P(x or y or z)

                                                      =P(x U y U z)

As the events are mutually exclusive

P(x U y U z)= P(x)+P(y)+P(z)

now P(x)= 1/3

P(y)=1/3

P(z)=1/3

P(x U y U z) = 1/3 + 1/3 + 1/3

                   = 3/3

                   =1

d)Finding probability of 1,4 or 7

Number of 1,4 or 7 cards in above sample set = 9

P(1,4 or 7) = P(1 U 4 U 7)

As the events are mutually exclusive

P(1,4 or 7) = P(1) + P(4) + P(7)

P(1)= 3/21

     =1/7

P(4)= 3/21

     =1/7

P(7)= 3/21

     =1/7

P(1,4 or 7)= 1/7 + 1/7 + 1/7

               =3/7

e)Finding probability of not striped

Number of not striped cards in above sample set = 14

P(not striped)= 14/21

                      = 2/3 !

B

Step-by-step explanation:

The standard form of equation of a circle is

(x-h)^2+(y-k)^2=r^2

Where h is x coordinate of the centre, k is the y coordinate of the centre and r is the radius of the circle

Hence given that h=5, k=-9 and r=12

So the above equation becomes

(x-5)^2+(y-(-9))^2=(12)^2

(x-5)^2+(y+9)^2=144

Hence the answer is B