Answer:
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
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 !