Two-similar-boxes-B-i-i-1-2-contain-i-1-red-and-5-i-1-black-balls-One-box-is-chosen-at-random-and-two-balls-are-drawn-randomly-what-is-the-probability-that-both-balls-are-of-different-colours-

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Question Number 12306 by Gaurav3651 last updated on 18/Apr/17

$$Twosimilarboxes{B}_i(i=1,2)contain$$$$(i+1)redand(5-i-1)blackballs.$$$$Oneboxischosenatrandomand$$$$twoballsaredrawnrandomly.$$$$whatistheprobabilitythatboth$$$$ballsareofdifferentcolours?$$$$\left(a\right)1/2$$$$\left(b\right)3/10$$$$\left(c\right)2/5$$$$\left(d\right)3/5$$

Answered by mrW1 last updated on 19/Apr/17

$$1\times \frac{2\times 3}{10}=\frac{3}{5}$$$$\Rightarrow \left(d\right)$$

Commented by Gaurav3651 last updated on 19/Apr/17

$$Sircanyoupleaseexplainthe$$$$solution.$$

Commented by mrW1 last updated on 19/Apr/17

$$Theanswershouldbe1\times \frac{6}{10}=\frac{3}{5},since$$$$itmakesnodifferencewhichboxis$$$$choosen.$$$$5ballsineachbox,3ballsincolourA$$$$and2ballsincolourB.$$$$$$$$possibilitiestotake2from5balls:$$$$C(5,2)=10$$$$possibilitiestotake2ballsindifferentcolours:$$$$2\times 3=6$$$$$$$$\Rightarrow 1\times \frac{6}{10}=\frac{3}{5}$$

Commented by Gaurav3651 last updated on 19/Apr/17

$$Thanksalotsir$$$$$$

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