Question

Total of 50 students

20 girls play lacrosse

20 boys play either soccer or lacrosse

20 students play soccer

what is the probability that a student plays soccer or is a girl?

Answer 1

The probability that a student plays soccer or is a girl = 0.8

Explanation:

Total number students playing soccer or lacrosse = 50 ......(1)

Number of boys playing soccer or lacrosse = 20 ........(2)

Number of students playing soccer = 20 .....(3)

`P(A) = (20)/(50)`

Number of girls who play lacrosse = 20 .....(4)

Number of students who play lacrosse = 50 - 20 = 30 ( From (1) and (3))

So, Number of boys playing lacrosse = 30 - 20 = 10 ( From (2))

Number of boys playing soccer = 20 - 10 = 10 (From (2))

So, Number of girls playing soccer = 20 - 10 = 10 (From (3))

`\text{P(A and B) = }(10)/(50)`

So, Total number of girls playing either soccer or lacrosse = 50 - 20 = 30

`\implies P(B) = (30)/(50)`

Now, we need to calculate P(A or B)

So, P(A or B) = P(A) + P(B) - P(A and B)

`\implies\text{P(A or B) = }(20)/(50)+(30)/(50)-(10)/(50)\\\\\implies\text{P(A or B) = }(40)/(50)=0.8`

Hence, The probability that a student plays soccer or is a girl = 0.8

Answer 2

Probability of student playing soccer, P(S) = 20/50 = 0.4
Probability of girls playing lacrosse, P(L) = 20/50 = 0.4

Probability of either playing soccer or being a girl = P(S or L) = P(S)+P(L) = 0.4+0.4 = 0.8