SOLUTION: Hi...I do my best in this Q and Try ..My email is toon_chy@yahoo.com. A package of Smarties contains 8 red, 7 yellow, 5 green, 3 orange, and 2 brown goodies. A little boy eats

Question 609521: Hi...I do my best in this Q and Try ..My email is toon_chy@yahoo.com.
A package of Smarties contains 8 red, 7 yellow, 5 green, 3 orange, and 2 brown goodies. A
little boy eats 7 of them at random. What is the probability that:
a. 3 are red
b. 3 are red, and 2 are yellow
c. At least 1 is orange
d. At least 1 is orange and 1 is brown
My answer..
a-if B (is the probability of 3 red)
P(B)=P(B/A)=3/7=O.4
b-if B (is the probability of 3 red)and C (is the probability of 2yellow)
P(B and C)=p(B).P(C)
P(B)=3/8=0.37 P(C)=2/7=0.28
P(B and C)=0.37*0.28=0.103
:.P(A and B and C)=p(A).P(B and C/P(A))=0.103
c- we used conditional and B is at lest 1 orange, P(A/B)=P(A and B)/P(B).
p(A and B)=P(A).P(B/A)= 0.28.((1/30)/0.28)=0.33
;. P(A/B)=0.33/(1/3)=0.1
d- I lost here
thx ...

Answer by ewatrrr(24785) (Show Source): You can put this solution on YOUR website!

 

Hi

A package of Smarties contains 8 red, 7 yellow, 5 green, 3 orange, and 2 brown goodies

 total... little boy eats 7 of them at random. 

 a. P(3 are red)= 8C3 *17C4 / 25C7 = 56*2380/480700

 b. 3 are red, and 2 are yellow =8C3* 7C2 *15C2 / 25C7

 c. At least 1 is orange = 1-P(no orange) = 1-22C7/ 25C7 = 1 - 170544/480700

 d. At least 1 is orange and 1 is brown =1-P(no orange or brown)) =1-20C7/25C7=1-77520/480700

Highly recommend using stattrek.com for Combinations Numbers, etc 

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