in a class of students, the following data table summarizes how many students play an instrument or a sport…

in a class of students, the following data table summarizes how many students play an instrument or a sport. what is the probability that a student who plays a sport also plays an instrument?\n| |plays an instrument|does not play an instrument|\n|--|--|--|\n|plays a sport|4|3|\n|does not play a sport|10|9|

in a class of students, the following data table summarizes how many students play an instrument or a sport. what is the probability that a student who plays a sport also plays an instrument?\n| |plays an instrument|does not play an instrument|\n|--|--|--|\n|plays a sport|4|3|\n|does not play a sport|10|9|

Answer

Explanation:

Step1: Find number of students who play a sport

The number of students who play a sport is the sum of those who play a sport and an instrument and those who play a sport but not an instrument. So, $4 + 3=7$.

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

The number of students who play a sport and an instrument is 4.

Step3: Calculate the conditional probability

The probability that a student who plays a sport also plays an instrument is the number of students who play a sport and an instrument divided by the number of students who play a sport. So the probability $P=\frac{4}{7}$.

Answer:

$\frac{4}{7}$