Federal health officials reported that a record number of to

Federal health officials reported that a record number of toddlers have received a full series of inoculations against nine diseases, including diphtheria, tetanus, measles, and mumps. The probability that a randomly selected toddler in Alabama has received a full set of inoculations is 0.823, it is 0.847 for a toddler in Georgia and 0.713 for a toddler in Utah. Suppose a toddler is independently selected from each of these three states is randomly selected.

(a) Find the probability that all three toddlers have received these inoculations.

(b) Find the probability that none of the three has received these inoculations.

(c) Find the probability that exactly one of the three toddlers has received these inoculations.

Solution

The probability that a randomly selected toddler in Alabama has received a full set of inoculations is 0.823, it is 0.847 for a toddler in Georgia and 0.713 for a toddler in Utah.

Consider here, Alabama = A , Georgia= B and Utah = C

note that all three events are independent.

P[ all three toddlers have received these inoculations. ]= 0.823*0.847*0.713 = 0.4970

b) A^c = 1-0.823=0.177

B^c = 1-0.847 = 0.153

C^c = 1 -0.713 = 0.287   

P[ none of the three has received these inoculations. ] = 0.177*0.153*0.287= 0.00777