for a certain class, the following data table compares how many students play an instrument or a sport. what…

for a certain class, the following data table compares how many students play an instrument or a sport. what is the probability that a student chosen randomly from the class plays a sport or an instrument?\n| |plays an instrument|does not play an instrument|\n|--|--|--|\n|plays a sport|4|2|\n|does not play a sport|5|9|

for a certain class, the following data table compares how many students play an instrument or a sport. what is the probability that a student chosen randomly from the class plays a sport or an instrument?\n| |plays an instrument|does not play an instrument|\n|--|--|--|\n|plays a sport|4|2|\n|does not play a sport|5|9|

Answer

Explanation:

Step1: Calculate total number of students

$4 + 2 + 5 + 9 = 20$

Step2: Find number of students who play a sport or an instrument

Use inclusion-exclusion principle: $(4 + 2) + (4 + 5) - 4 = 6 + 9 - 4 = 11$

Step3: Compute the probability

$\frac{\text{Number of favorable students}}{\text{Total number of students}} = \frac{11}{20}$

Answer:

$\frac{11}{20}$