Question

Data collected at elementary schools in a certain county in the US suggest that each year roughly 25% of students miss exactly one day of school, 14% miss 2 days, and 26% miss 3 or more days due to sickness. a. What is the probability that a student chosen at random doesn't miss any days of school due to sickness this year? (Enter your answer to two decimal places.) b. What is the probability that a student chosen at random misses no more than one day? (Enter your answer to two decimal places.) c. What is the probability that a student chosen at random misses at least one day? (Enter your answer to two decimal places.) d. If a parent has two kids at an elementary school in this county, what is the probability that neither kid will miss any school? Assume the probabilities are independent. (Enter your answer to four decimal places.) e. If a parent has two kids at an elementary school in this county, what is the probability that both kids will miss some school, i.e., at least one day? Assume the probabilities are independent. (Enter your answer to four decimal places.) f. Do you think it was reasonable to assume the probabilities are independent in parts (d) and (e)? The kids are siblings, and if one gets sick it probably ... the chance that the other one gets sick. So whether or not one misses school due to sickness is probably ... of the other

Answer 1

Data collected at elementary schools in DeKalb County, GA suggest that each year roughly 25% of students miss exactly one day of school, 14% miss 2 days, and 26% miss 3 or more days due to sickness.

Solution:

a) the probability that a student chosen at random doesn't miss any days of school due to sickness :

probability does not miss = P(X = 0)

P(X = 0) =1-0.25 - 0.14 - 0.26

=0.35

b) the probability that a student chosen at random misses no more than one day :

P(X≤1) = P(X=0) + P(X=1)

= 0.35 + 0.25

= 0.60

c) the probability that a student chosen at random misses at least one day:

P(X≥1) = 1- P(X=0)

= 1- 0.35

= 0.65

d) If a parent has two kids at an elementary school, the probability that neither kid will miss any school :

Assume that events are independent,

Therefore, Probability that neither kid miss any school

= 0.35 * 0.35

= 0.1225

e) If a parent has two kids at an elementary school, the probability that both kids will miss some school, ie at least one day:

probabilty that both kids miss some school

= (1 - 0.35)*(1 - 0.35)

= 0.65 * 0.65

= 0.4225

f) Do you think it was reasonable to assume the probabilities are independent in parts (d) and (e)? The kids are siblings, and if one gets sick it probably ... the chance that the other one gets sick. So whether or not one misses school due to sickness is probably ... of the other

we assumed that going to school probability for both kids is independent of each other, That does not seem much reasonable as being kids of same parent their school going tendency should be positivily correlated.