Can you help me with this statistics and probability questions please?

[JordynC]

30. A typical box of smarts contains 48 of the candy coated treats. There are eight of each (red, orange, yellow, brown, blue, green, pink, and violet). Each colour is equally likely.

a. If you pour a handful (13 smarties) into your friends palm, what is the probability to get 4 orange smarties in the mix she receives. Note: This is sampling without replacement.

b. calculate the expected number of orange smarties she will have in her handful.

 

[Deleted member 4993]

30. A typical box of smarts contains 48 of the candy coated treats. There are eight of each (red, orange, yellow, brown, blue, green, pink, and violet). Each colour is equally likely.

a. If you pour a handful (13 smarties) into your friends palm, what is the probability to get 4 orange smarties in the mix she receives. Note: This is sampling without replacement.

b. calculate the expected number of orange smarties she will have in her handful.

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[lex]

part (b) is certainly easy: [MATH]\frac{13}{8} \hspace2ex[/MATH] (by symmetry)

 

[lex]

For completeness:
(assuming exactly 4 orange)

part (a) [MATH]\frac{\binom{15}{6}-7\binom{8}{6}} {\binom{20}{7}-8\binom{13}{7}}[/MATH]
part (b) [MATH]\frac{13}{8}\hspace1ex[/MATH] by symmetry