Answer:
The probability that a student plays soccer or is a girl = 0.8
Step-by-step 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)
[tex]P(A) = \frac{20}{50}[/tex]
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))
[tex]\text{P(A and B) = }\frac{10}{50}[/tex]
So, Total number of girls playing either soccer or lacrosse = 50 - 20 = 30
[tex]\implies P(B) = \frac{30}{50}[/tex]
Now, we need to calculate P(A or B)
So, P(A or B) = P(A) + P(B) - P(A and B)
[tex]\implies\text{P(A or B) = }\frac{20}{50}+\frac{30}{50}-\frac{10}{50}\\\\\implies\text{P(A or B) = }\frac{40}{50}=0.8[/tex]
Hence, The probability that a student plays soccer or is a girl = 0.8
