Answer to Question #144821 in Statistics and Probability for Cameron Foster

Question

Instructor Sara sends five random Class VII students to Nord for a field study. Currently, Class VII
contains six girls and eight boys. Please find the following. Keep your solutions exact to four decimal
places if needed.
(a) Calculate the sample space
(b) Find the probability if Sara sends only girls.
(c) Find the probability if Sara sends only boys.
(d) Find the probability if Sara sends three girls.
(e) Find the probability if Sara sends three boys.

Answer 1

(a) $S = \{g, b\}$

$P(b) = 8/14 \\ P(g) = 6/14$

$n(s) = C(14, 5) = 2002$

(b) Only girls = 5 girls and 0 boys = $C(8,0) × C(6,5)$

= $1 × 6= 6$

P(only girls) = 6/2002 = 3/1001

P(only girls) = 0.002997

(c) Only boys = 0 girls and 5 boys = $C(6,0) × C(8,5)$

$= 56× 1$

P(only boys) = 56/2002 = 4/143

P(only boys) = 0.02797

(d) 3 girls and 2 boys =

$C(6, 3) × C(8, 2)$

$=560$

P(3 girls) = 560/2002 = 40/143

P(3 girls) = 0.2797

(e) 3 boys amd 2 girls =

$C(8,3) × C(6,2)$

$= 840$

P(3 boys) = 840/2002 = 60/143

P(3 boys) = 0.4196