Menu Close

Question-87418




Question Number 87418 by liki last updated on 04/Apr/20
Answered by Rio Michael last updated on 04/Apr/20
(a) since we have 3 match pairs in the box, then  P(match pair) = (1/3).   (b) we have six socks in that box, 3 left feet and 3 right fit         P(left feet) = (1/3) and P(right feet) = (1/3)    ⇒ P(left and right) = (1/3) × (1/3) = (1/9) since they are independent events   (c) P(2 socks of right feet) = (2/3)  (d) P(RR or LL) = (1/9) + (1/9) = (2/9)
$$\left(\mathrm{a}\right)\:\mathrm{since}\:\mathrm{we}\:\mathrm{have}\:\mathrm{3}\:\mathrm{match}\:\mathrm{pairs}\:\mathrm{in}\:\mathrm{the}\:\mathrm{box},\:\mathrm{then} \\ $$$$\mathrm{P}\left(\mathrm{match}\:\mathrm{pair}\right)\:=\:\frac{\mathrm{1}}{\mathrm{3}}. \\ $$$$\:\left(\mathrm{b}\right)\:\mathrm{we}\:\mathrm{have}\:\mathrm{six}\:\mathrm{socks}\:\mathrm{in}\:\mathrm{that}\:\mathrm{box},\:\mathrm{3}\:\mathrm{left}\:\mathrm{feet}\:\mathrm{and}\:\mathrm{3}\:\mathrm{right}\:\mathrm{fit} \\ $$$$\:\:\:\:\:\:\:\mathrm{P}\left(\mathrm{left}\:\mathrm{feet}\right)\:=\:\frac{\mathrm{1}}{\mathrm{3}}\:\mathrm{and}\:\mathrm{P}\left(\mathrm{right}\:\mathrm{feet}\right)\:=\:\frac{\mathrm{1}}{\mathrm{3}} \\ $$$$\:\:\Rightarrow\:\mathrm{P}\left(\mathrm{left}\:\mathrm{and}\:\mathrm{right}\right)\:=\:\frac{\mathrm{1}}{\mathrm{3}}\:×\:\frac{\mathrm{1}}{\mathrm{3}}\:=\:\frac{\mathrm{1}}{\mathrm{9}}\:\mathrm{since}\:\mathrm{they}\:\mathrm{are}\:\mathrm{independent}\:\mathrm{events} \\ $$$$\:\left(\mathrm{c}\right)\:\mathrm{P}\left(\mathrm{2}\:\mathrm{socks}\:\mathrm{of}\:\mathrm{right}\:\mathrm{feet}\right)\:=\:\frac{\mathrm{2}}{\mathrm{3}} \\ $$$$\left(\mathrm{d}\right)\:\mathrm{P}\left(\mathrm{RR}\:\mathrm{or}\:\mathrm{LL}\right)\:=\:\frac{\mathrm{1}}{\mathrm{9}}\:+\:\frac{\mathrm{1}}{\mathrm{9}}\:=\:\frac{\mathrm{2}}{\mathrm{9}} \\ $$
Commented by liki last updated on 04/Apr/20
....thank you sir,
$$….{thank}\:{you}\:{sir}, \\ $$

Leave a Reply

Your email address will not be published. Required fields are marked *