Question

A school has 200 seniors of whom 140 will be going to college next year. Forty will be going directly to work. The remainder are taking a gap year. Fifty of the seniors going to college play sports. Thirty of the seniors going directly to work play sports. Five of the seniors taking a gap year play sports. What is the probability that a senior is going to college and plays sports?

Short answer

Probability that senior goes to college & plays sports = 1 / 4

Step-by-step solution

Given Information

Total $200$students

localid="1650302556929" $140$going to college & $50$among these play sports ; $40$going to work & localid="1650302575847" $30$of these play sports

• Remaining ie $200-140-40=20$taking a gap & 5 among them play sports

Formula & Numerical Solution 

Probability is the likelihood of an event, calculated as follow:

favorable outcomes / total outcomes

Probability that a senior is going to college and plays sports

$=\mathrm{Seniors}\mathrm{going}\mathrm{to}\mathrm{college}\&\mathrm{playing}\mathrm{sports}/\mathrm{total}\mathrm{seniors}=\frac{50}{200}=\frac{1}{4}$