Kiran surveyed a random sample of students in her school district, and she found these statistics: p{rides bike to school})=0.1 p{has crossing guard})=0.48 p{rides bike and crossing guard})=0.12 find the probability that a student rides a bike to school, given that the student's school has a crossing guard.

You can use the chain rule of probability.

The probability that a student rides a bike to school, given that the student's school has a crossing guard is given by 0.25

For two events A and B, we have:

Probability that event A or B occurs = Probability that event A occurs + Probability that event B occurs - Probability that both the event A and B occur simultaneously.

This can be written symbolically as:

For two events A and B:

The chain rule states that the probability that A and B both occur is given by:

You can remember this fact by using a trick that when A is on left, it is behind B in next term P(A)P(B|A)

And when B is on left, then it is behind A in next term P(B)P(A|B)

P(A|B) = Probability that A will happen given B has already happened.

P(B|A) = Probability that B will happen given A has already happened.

Let the event A be that a student rides bike to school.

Let the event B be that the student's school has a crossing guard

Then we are given that:

P(A) = P{rides bike to school})=0.1

P(B) = P{has crossing guard})=0.48

= P{rides bike and crossing guard})=0.12

We have to find P(a student rides a bike to school, given that the student's school has a crossing guard) = P(A | B)

From the chain rule of probability, we have:

Thus,

Thus,

The probability that a student rides a bike to school, given that the student's school has a crossing guard is given by 0.25

Learn more about conditional probability here:

link

.25

Step-by-step explanation:

P(rides bike ∣ crossing guard) =

P(has crossing guard) / P(rides bike and crossing guard)

P(has crossing guard) / P(rides bike and crossing guard) = 0.12 / 0.48 = 1 / 4 = 0.25

P(rides bike ∣ crossing guard) = 1/4 = 0.25

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step-by-step explanatio89