Answer to Question #6107 in Statistics and Probability for malissa

Question

Malissa has a red,blue,green, and yellow sweater. Jill has a green, red, purple, and white sweater, Emily has a re, blue, purple, and mauve sweater. Each girl has only one sweater of each color, and will pivk a sweater to wear at random.
1. P(each girl chooses a different color)
2. P(each girl chooses the same color)
3. P(two girls choose the same color, and the third chooses a different color)
4. P(each girl chooses a red sweater)

Answer 1

So Malissa(name M) has r,b,g,y
Jill (J) has r,g,p,w
Emily(E) has & r,b,p,m
1. P(each girl chooses a different color)
Here are oll combinations of choosen sweeters when they all are different.first letter-colour of sweeter of 1st girl etc.
Rgb, rgp, rgm, rpb, rpm, rwb, rwp, rwm,
Brp, brm, bgr,bgp,bgm,bpr,bpm,bwr,bwp,bwm,
Grb,grp,grm,gpr,gpb,gpm,gwr,gwb,gwp,gwm,
Yrb,yrp,yrm,yg(r,b,p,m), yp(r,b,m),yw(r,b,p,m)
Total combinations: 42/64=21/32

2. P(each girl chooses the same color)=1/4*4*4=1/64, cuz there is only one variant(r,r,r) out of 4*4*4
3. P(two girls choose the same color, and the third chooses a different color)
It could be r,r, and any other colour for 3rd girl except red, or b,b or& gg& or& pp and for 3rd girl- 4 variants
So total: 3*1*3+3*1*4=9+12 variants& so P=21/64
4. P(each girl chooses a red sweater)= P(each girl chooses the same color)=1/4*4*4=1/64, cuz there is only one variant(r,r,r) out of 4*4*4