Assume that the box contains 6 balls 2 white 2 yellow and 2

Assume that the box contains 6 balls: 2 white, 2 yellow, and 2 blue. Balls are drawn in succession without replacement, and their colors are noted until a white ball is drawn. How many outcomes are there in the sample space?

Solution

There are going to be 5 cases.

Case 1: First Ball drawn is white

Number of outcomes = 1(W)

Case 2: Second ball drawn is white.

Number of outcomes = 2(Y,B)

Case 3: Third ball drawn is white.

Number of outcomes = 4(YY,YB,BY,BB)

Case 4: Fourth ball is white.

Number of outcomes = 6 (YYB,YBY,YBB,BYY,BYB,BBY)

Case 5 : fifth ball drawn is white.

Number of outcomes = 6 (YYBB,YBBY,BBYY,BYBY,BYYB,YBYB)

Total number of outcomes = 1 + 2 + 4 + 6 + 6 = 19