it is assumed that when children are born they are equally likely to be boys or girls. what is the probability that a family of four children constains (a)three boys and girl (b)two boys and two girls Mr W pls help out


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Question Number 140344 by mathdave last updated on 06/May/21

$i t i s a s s u m e d t h a t w h e n c h i l d r e n a r e b o r n t h e y$ $a r e e q u a l l y l i k e l y t o b e b o y s o r g i r l s .$ $w h a t i s t h e p r o b a b i l i t y t h a t a f a m i l y$ $o f f o u r c h i l d r e n c o n s t a i n s$ $(a) t h r e e b o y s a n d g i r l$ $(b) t w o b o y s a n d t w o g i r l s$ $M r W p l s h e l p o u t$
	Answered by mr W last updated on 06/May/21

	$(a)$ $p r o b a b i l i t y f o r a c h i l d t o b e g i r l i s \frac{1}{2},$ $p r o b a b i l i t y f o r o n e f r o m 4 c h i l d r e n$ $t o b e g i r l i s t h e n$ $p = C_{1}^{4} \times \frac{1}{2^{4}} = \frac{1}{4}$ $(b)$ $p = C_{2}^{4} \times \frac{1}{2^{4}} = \frac{3}{8}$
	Commented by mathdave last updated on 06/May/21

	$t h a n k s s o m u c h b u t p l s c a n u t e l l m e h w u g o t$ $C_{1}^{4} a n d \frac{1}{2^{4}}, C_{2}^{4} a n d \frac{1}{2^{4}}$
	Commented by mr W last updated on 06/May/21

	$y o u s h o u l d r e a d a b o u t b i n o m i a l$ $p r o b a b i l i t y .$
	Commented by mr W last updated on 06/May/21

	Commented by mr W last updated on 06/May/21

	$c e r t a i n l y w e c a n a l s o s o l v e i n o t h e r$ $w a y s .$ $f o u r d i f f e r e n t c h i l d e n, e a c h c a n b e$ $b o y o r g i r l, t h e r e a r e t o t a l l y 2^{4}$ $p o s s i b i l i t i e s .$ $(a)$ $o n e c h i l d i s g i r l, t h e r e a r e C_{1}^{4} = 4$ $p o s s i b i l i t i e s, i . e .$ $1 2 3 4$ $G B B B$ $B G B B$ $B B G B$ $B B B G$ $s o t h e p r o b a b i l i t y i s \frac{4}{2^{4}} = \frac{1}{4} .$ $(b)$ $t w o c h i l d r e n a r e b o y s, t h e r e a r e$ $C_{2}^{4} = 6 p o s s i b i l i t i e s, i . e .$ $1 2 3 4$ $B B G G$ $B G B G$ $B G G B$ $G B B G$ $G B G B$ $G G B B$ $p r o b a b i l i t y i s \frac{6}{2^{4}} = \frac{3}{8}$
	Commented by Tawa11 last updated on 06/Sep/21

	$Great sir$
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