a box contains 20 red,30 black,40 blue,50 white. what will be the minimum number of balls to be drawn without replacement so that you are certain about getting 4 red,5 black,6 blue,7 white balls?
A.140
B.97
C.104
D.124
Answered by MathMate a few days ago under a Physics heading
http://www.jiskha.com/display.cgi?id=1403632512
To determine the minimum number of balls to be drawn without replacement to guarantee obtaining a specific number of each color, we can calculate the sum of the required numbers of each color and add 1.
Let's consider the worst-case scenario, where we draw all the other colors first before obtaining the desired numbers of each color. In this case, we would need to draw:
4 red balls + 5 black balls + 6 blue balls + 7 white balls = 22 balls
However, we must add 1 to this number to ensure that we have the exact number of each color guaranteed. Therefore, the minimum number of balls to be drawn without replacement to guarantee getting 4 red, 5 black, 6 blue, and 7 white balls is:
22 + 1 = 23
Therefore, the correct answer is not listed in the options given. None of the answers A. 140, B. 97, C. 104, or D. 124 is correct.
To be certain about getting 4 red, 5 black, 6 blue, and 7 white balls, we need to calculate the worst-case scenario, where we draw the balls of other colors before the desired number of each color is reached.
Step 1: Calculate the number of balls needed to reach each desired color:
4 red + 5 black + 6 blue + 7 white = 22 balls
Step 2: Calculate the number of balls in the box:
20 red + 30 black + 40 blue + 50 white = 140 balls
Step 3: Subtract the number of balls in the box from the number of balls needed:
22 balls - 140 balls = -118 balls
Since we can't have a negative number of balls, we need to redraw some balls. The minimum number of balls we need to redraw is equal to the absolute value of -118:
|-118| = 118
Step 4: Add the minimum number of balls needed to redraw to the total number of balls:
140 balls + 118 balls = 258
Therefore, the minimum number of balls that need to be drawn without replacement is 258.
The correct answer is not provided among the options.