Question

Sheila either walks or cycles to school.
The probability that she walks to school is 0.65
If she walks, the probability that she is late is 0.4
If she cycles, the probability that she is late is 0.1
What is the probability that on any one day she is not late

Answer 1

Answer:0.705

Step-by-step explanation:

walks=0.65 and is late=0.4;is not late=0.6

cycles=0.35 and is late=0.1;is not late=0.9

so if you need to find the probability of sheila walking and not being late:

0.65*0.6=0.39

AND probability of being not late and cycling:

0.35*0.9=0.315

therefore,the probability of sheila walking or cycling and still not being late:

0.39+0.315=0.705

Answer 2

Given: Sheila either walks or cycles to school. The probability that she walks to school is 0.65

If she walks, the probability that she is late is 0.4

If she cycles, the probability that she is late is 0.1.

To find: Probability that on any one day she is not late to school

Solution: Let P(E1) be the probability that she walks to school and P(E2) be the probability that she cycles to school.

P(E1)= 0.65

Since she has only two options of either walking or cycling to school, therefore:

P(E2) = 1 - P(E1)

P(E2) = 1-0.65

= 0.35

Let P(A) be the probability that she is late.

Therefore,

P(A/E1) = Probability that she is late when she walks to school

= 0.4

P(A/E2) = Probability that she is late when she cycles to school

= 0.1

Here, total probability theorem is used to determine the probability of being late to school.

Total probability theorem is given by the formula:

P(A) = P(A/E1) × P(E1) + P(A/E2) × P(E2)

= 0.4 × 0.65 + 0.1 × 0.35

= 0.26 + 0.035

= 0.295

Therefore, probability that she is late is 0.295.

Probability that she is not late to school

= 1 - Probability that she is late to school

= 1- 0.295

= 0.705

Therefore, the probability that on any day she is not late is 0.705 .