At a new exhibit in the Museum of Science, people are asked to choose between 50

Question

At a new exhibit in the Museum of Science, people are asked to choose between 50 or 100 random draws from a machine. The machine is known to have 60 green balls and 40 red balls. After each draw, the color of the ball is noted and the ball is put back for the next draw. You win a prize if more than 70% of the draws result in a green ball.

Calculate the probability of getting more than 70% green balls. (Round intermediate calculations to 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places).

Would you choose 50 or 100 draws for the game?

50 Balls or 100 Balls?

Explanation / Answer

At a new exhibit in the Museum of Science, people are asked to choose between 50 or 100 random draws from a machine. The machine is known to have 60 green balls and 40 red balls. After each draw, the color of the ball is noted and the ball is put back for the next draw. You win a prize if more than 70% of the draws result in a green ball.

Calculate the probability of getting more than 70% green balls. (Round intermediate calculations to 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places).

n

Probability

50

0.0749

100

0.0207

Would you choose 50 or 100 draws for the game?

50 Balls or 100 Balls?

Probability of green ball =0.6

For n=50, sd=sqrt(0.6*0.4/50) =0.0693

Z value for 70% or 0.7, z=(0.7-0.6)/0.0693 =1.44

P( p>0.7) =P( z >1.44) =0.0749

For n=100, sd=sqrt(0.6*0.4/100) =0.0490

Z value for 70% or 0.7, z=(0.7-0.6)/0.0490 =2.04

P( p>0.7) =P( z >2.04) = 0.0207

We choose 50 draws for the game because probability for 50 game is large.

n

Probability

50

0.0749

100

0.0207

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