jimmie has 7 brown marbles,4 blue marbles and 9 red marbles in a bag. What is the probability that jimmie will select two red marbles without replacement?

Question

jimmie has 7 brown marbles,4 blue marbles and 9 red marbles in a bag. What is the probability that jimmie will select two red marbles without replacement?

Answer 1

Good morning Dj,

The probability Jimmie draws a red marble first is 9/20. Why? The numerator represents the total number of red marbles, and the denominator the total number of marbles in the bag. 

Since you are not replacing the marble, that leaves all of the marbles in the bag minus one that Jimmie just took out,  meaning the probability of Jimmie drawing a red marble on the second draw is going to be 8/19.  Why? Assuming Jimmie drew a red marble, that leaves eight red marbles left. Also, drawing one marble without replacing leaves only 19 marbles left in the bag. 

Now, multiply the two probabilities in fraction form because probabilities are always expressed as percentages. 

9/20 * 8/19 = 72/380  

Now you need to simplify this fraction by dividing both the numerator and denominator by the greatest or highest common denominator which is 4. 

When dividing the numerator and denominator by 4 the new fraction is 18/95.  

To obtain the decimal version of this fraction simply divide the numerator by the denominator, that is 18 by 95 and you arrive at a probability in decimal form 0.189474 (rounded to six decimal places as is usual in these exercises). 

I hope this assists and you have a great day today. Please feel free to ask for clarification, further questions, or feedback in the comment section below. 

I hope this assists you and that you have a great day today.