In a class of 30 girls, 13 are dancers and 23 are gymnasts. If 7 girls do both dance and gymnastics, what is the probability that a girl chosen at random does neither dance nor gymnsatics.
Answer: 1/30
Thanks to anyone who helps
Only Dance = 13- 7 = 6
Only Gym = 23-7 = 16
both = 7
sum = 6 + 16 + 7 = 29
30 - 29 = 1
One does neither
To find the probability that a girl chosen at random does neither dance nor gymnastics, we need to determine the number of girls who do neither activity and divide it by the total number of girls in the class.
Given:
Number of girls in the class = 30
Number of girls who dance = 13
Number of girls who do gymnastics = 23
Number of girls who do both dance and gymnastics = 7
To find the number of girls who do neither activity, we can subtract the total number of girls who do either dance or gymnastics or both from the total number of girls in the class.
Total number of girls who do either dance or gymnastics = Number of girls who dance + Number of girls who do gymnastics - Number of girls who do both dance and gymnastics
= 13 + 23 - 7
= 29
Now, we can determine the probability by dividing the number of girls who do neither activity (1) by the total number of girls in the class (30):
Probability = Number of girls who do neither activity / Total number of girls in the class
= 1 / 30
Therefore, the probability that a girl chosen at random does neither dance nor gymnastics is 1/30.