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Pleaseee helP
Find the indicated conditional probability
using the following two-way table:
Grade
Drive to school
Take the bus
Walk
Sophomore
2
25
3
Junior
13
20
2
Senior
25
5
5
P( Drive to school | Sophomore ) = [?]

Pleaseee HelP Find The Indicated Conditional Probability Using The Following Twoway Table Grade Drive To School Take The Bus Walk Sophomore 2 25 3 Junior 13 20 class=

Sagot :

semsee45

Answer:

P(Drive to school | Sophomore) = 0.07 (nearest hundredth)

Step-by-step explanation:

A probability is conditional if it depends on what has already happened.

P(Drive to school | Sophomore) means:

The probability that a student "drives to school" given that they are a "sophomore".

Using the conditional probability formula:

P(B | A) = P(B ∩ A) ÷ P(A)

⇒  P(Drive to school | Sophomore) = P(Drive to school ∩ Sophomore) ÷ P(Sophomore)

Reading from the two-way table, there are 2 people that drive to school AND are a sophomore.

Adding all the values in the table gives us the total number of students: 2 + 13 + 25 + 25 + 20 + 5 + 3 + 2 + 5 = 100

⇒ P(Drive to school ∩ Sophomore) = 2/100 = 0.02

Adding all the values in the sophomore line of the table gives us the total number of sophomores:  2 + 25 + 5 = 30

⇒ P(Sophomore) = 30/100 = 0.3

Now plug these values into the formula:

P(Drive to school | Sophomore)  = P(Drive to school ∩ Sophomore) ÷ P(Sophomore)

P(Drive to school | Sophomore)  = 0.02 ÷ 0.3

                                                      = 1/15

                                                      = 0.07 (nearest hundredth)

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