Question

mrs. broady has a large bag filled with red and green cards. she tells the class that 15% of the cards are red and 85% are green. at the end of each class, she mixes the cards, reaches inside the bag, and draws out one card at random. if a red card is drawn, the students will not be assigned homework. she shows the class the card, and then places the card back in the bag. carla would like to carry out a simulation to estimate the number of days it will take in order to get a no homework day. she assigns the digits to the outcomes.
00 - 14 = red
15 - 99 = green
here is a portion of a random number table.
beginning at line 1 and starting each new trial right after the previous trial, carry out 5 trials of this simulation. based on these 5 trials, what is the average number of days it will take to get a no homework day?

Explanation:

Step1: Analyze the first trial

For the first trial, we look at the numbers in line 1: 31640. We take two - digit numbers. The first two - digit number is 31 (not in 00 - 14), then 64 (not in 00 - 14), then 40 (not in 00 - 14), then 03 (in 00 - 14). The number of days in the first trial is 4.

Step2: Analyze the second trial

For the second trial, we continue from where the first trial left off. The next numbers are 407. The two - digit numbers: 40 (not in 00 - 14), 07 (in 00 - 14). The number of days in the second trial is 2.

Step3: Analyze the third trial

For the third trial, we continue. The numbers are 96193. The two - digit numbers: 96 (not in 00 - 14), 61 (not in 00 - 14), 19 (not in 00 - 14), 93 (not in 00 - 14), 10 (in 00 - 14). The number of days in the third trial is 5.

Step4: Analyze the fourth trial

For the fourth trial, we continue. The numbers are 898. The two - digit numbers: 89 (not in 00 - 14), 98 (not in 00 - 14), 80 (not in 00 - 14), 85 (not in 00 - 14), 32 (not in 00 - 14), 71 (not in 00 - 14), 16 (not in 00 - 14), 69 (not in 00 - 14). Wait, no, we should group as two - digit numbers from the start of the new trial. The new trial starts with 10898. The two - digit numbers: 10 (in 00 - 14). The number of days in the fourth trial is 1.

Step5: Analyze the fifth trial

For the fifth trial, we continue. The numbers are 08532. The two - digit numbers: 08 (in 00 - 14). The number of days in the fifth trial is 1.

The sum of the number of days in the 5 trials is \(4 + 2+5 + 1+1=13\).

The average number of days is \(\frac{13}{5}=2.6\)

Answer:

\(2.6\)