Question

The probability that a student at your school takes Drivers Education and Spanish is 87/1000. The probability that a student takes Spanish is 68/100

what is the probability they are in both in simplest form??

Answer 1

let

x---------> The probability that a student takes Spanish

y-------> the probability that a student takes Drivers Education given that the Student is taking Spanish

z-------> The probability that a student at school takes Drivers Education and Spanish

we know that

`z=x* y`------> solve for y

`y=(z)/(x)`

`z=(87)/(1000)`

`x=(68)/(100)`

substitute

`y=\huge \text((87)/(1000)/ (68)/(100) \huge \text{)}\implies y=(87)/(680)`

the answer is

87/680

Answer 2

Let the probability that a student takes Drivers Education be represented by P(D) and the probability that a student takes Spanish be represented by P(S).

We are given that:
P(D and S) = 87/1000
P(S) = 68/100

We can use the formula:
P(D and S) = P(D) * P(S|D)
where P(S|D) is the conditional probability of taking Spanish given that the student is already taking Drivers Education.

We can rearrange the formula to solve for P(S|D):
P(S|D) = P(D and S) / P(D)

Substituting in the given values:
P(S|D) = (87/1000) / P(D)

We can also use the formula:
P(D and S) = P(S) * P(D|S)
where P(D|S) is the conditional probability of taking Drivers Education given that the student is already taking Spanish.

We can rearrange the formula to solve for P(D|S):
P(D|S) = P(D and S) / P(S)

Substituting in the given values:
P(D|S) = (87/1000) / (68/100)

Simplifying:
P(S|D) = 87/680
P(D|S) = 87/68

Therefore, the probability that a student is taking both Drivers Education and Spanish is:
P(D and S) = P(D) * P(S|D) = P(S) * P(D|S)
P(D and S) = (68/100) * (87/680) = (1/5) * (87/680) = 87/3400

So the probability that a student takes both Drivers Education and Spanish in simplest form is 87/3400.