A box contains one black and one white ball. Two balls are drawn with replacemen

Question

A box contains one black and one white ball. Two balls are drawn with replacement, i.e. a ball is drawn, its color noted and the ball is then replaced in the box. The sample space for this experiment could be written as S = {(BB)}, (BW), (WW)}. Are these three elementary events equally likely? How would you write the sample space in order to make all elementary events equally likely? How could you write a sample space with equally likely elementary, if there were one black and two white balls in the box?

Explanation / Answer

A box contains 2 balls with one black and one white colour. Two balls are selected with replacement means a ball is selected its colour is noted and it is kept in box.

The possible outcome of event is BB, WW, BW

S = {(BB), (BW), (WW)}

Elementary event is a single outcome of the sample space, so here elemenatry event is

Elementary events E1 ={BB}, E2= {BW}, E3={WW}

Here there exists one more outcome in the sample space which is WB hence the elementary events of given sample space is not equally likely.

b) Inorder to be each elementary event equally likely the sample space can be written as

S ={(BB), (BW), (WB),(WW)}

c)The sample space with equally likely elementary events for one balck and two white balls is

Let label two white balls as W1 and W2 so the sample space is

S={(BW1),(BW2), (BB), (W1B),(W2B),(W1W2)}

where each elementary event the above sample space is equally likely i.e. the each single outcome of sample sapce have same chance to occur.

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