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Jamie wakes up late on average 1 days out of every 5. If Jamie wakes up late, the probability that she is late for school is 80%. If Jamie doesn't wake up late the probability that she is late for school is 35%. Create a tree diagram by entering the percentages and then calculate the percent chance that Jamie gets to school on time. Enter your answers as a decimal or fraction between 0 and 1. Late On time Late On time Late On time A B C D E F Wake up Get to School [Graphs generated by this script: setBorder(0);initPicture(-8.3,5.5);strokewidth = '2';marker = 'arrow';line([-8,0], [-3,2]);line([-8,0], [-3,-2]);line([0,2], [2,3]);line([0,2], [2,1]);line([0,-2], [2,-1]);line([0,-2], [2,-3]);text([-1.7,2], 'Late');text([-1.6,-2], 'On time');text([4,3], 'Late');text([4,1], 'On time');text([4,-1], 'Late');text([4,-3], 'On time');fontweight = 'bold';text([-6,1.5], 'A');text([-6,-1.5], 'B');text([.7,2.8], 'C');text([.7,1.3], 'D');text([.7,-1.3], 'E');text([.7,-2.9], 'F');text([-1.6,4], 'Wake up');text([4,4], 'Get to School');] Place your percentages here: C: A: D: B: E: F: The percent chance (as a decimal) that Jamie gets to school on time:

Question

Jamie wakes up late on average 1 days out of every 5. If Jamie wakes up late, the probability that she is late for school is 80%. If Jamie doesn't wake up late the probability that she is late for school is 35%. Create a tree diagram by entering the percentages and then calculate the percent chance that Jamie gets to school on time. Enter your answers as a decimal or fraction between 0 and 1. Late On time Late On time Late On time A B C D E F Wake up Get to School [Graphs generated by this script: setBorder(0);initPicture(-8.3,5.5);strokewidth = '2';marker = 'arrow';line([-8,0], [-3,2]);line([-8,0], [-3,-2]);line([0,2], [2,3]);line([0,2], [2,1]);line([0,-2], [2,-1]);line([0,-2], [2,-3]);text([-1.7,2], 'Late');text([-1.6,-2], 'On time');text([4,3], 'Late');text([4,1], 'On time');text([4,-1], 'Late');text([4,-3], 'On time');fontweight = 'bold';text([-6,1.5], 'A');text([-6,-1.5], 'B');text([.7,2.8], 'C');text([.7,1.3], 'D');text([.7,-1.3], 'E');text([.7,-2.9], 'F');text([-1.6,4], 'Wake up');text([4,4], 'Get to School');] Place your percentages here:

C: 

A: D: B: E: F: The percent chance (as a decimal) that Jamie gets to school on time:

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Solution

The tree diagram can be filled as follows:

A: 0.2 (Probability Jamie wakes up late) B: 0.8 (Probability Jamie wakes up on time) C: 0.8 (Probability Jamie is late for school if she wakes up late) D: 0.2 (Probability Jamie is on time for school if she wakes up late) E: 0.35 (Probability Jamie is late for school if she wakes up on time) F: 0.65 (Probability Jamie is on time for school if she wakes up on time)

To calculate the overall probability that Jamie gets to school on time, we need to consider both scenarios where she could be on time: when she wakes up late and still manages to get to school on time, and when she wakes up on time and gets to school on time.

This can be calculated as follows:

(A * D) + (B * F) = (0.2 * 0.2) + (0.8 * 0.65) = 0.04 + 0.52 = 0.56

So, the percent chance (as a decimal) that Jamie gets to school on time is 0.56 or 56%.

This problem has been solved

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