There are 4 children in the team. Find the probability that three are girls and one is a boy.


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Question Number 139940 by mathdanisur last updated on 02/May/21

$T h e r e a r e 4 c h i l d r e n i n t h e t e a m .$ $F i n d t h e p r o b a b i l i t y t h a t t h r e e a r e$ $g i r l s a n d o n e i s a b o y .$
	Answered by mr W last updated on 02/May/21

	$c h i l d r e n a r e d i f f e r e n t :$ $c h i l d 1, c h i l d 2, c h i l d 3, c h i l d 4 .$ $t o t a l : 2^{4} = 16$ $o n e i s b o y (= t h r e e a r e g i r l s) : 4$ $\Rightarrow p = \frac{4}{16} = \frac{1}{4}$
	Commented by mr W last updated on 02/May/21

	$o r$ $p r o b a b i l i t y f o r e a c h c h i l d t o b e g i r l : \frac{1}{2}$ $p r o b a b i l i t y f o r n c h i l d r e n t o b e g i r l :$ $(\begin{matrix} 4 \\ n \end{matrix}) {(\frac{1}{2})}^{4}$ $n = 3 : p = (\begin{matrix} 4 \\ 3 \end{matrix}) {(\frac{1}{2})}^{4} = \frac{4}{16} = \frac{1}{4}$
	Commented by mathdanisur last updated on 02/May/21

	$t h a n k s S i r$
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