76% of toddlers get their immunization. Suppose that 6 toddlers are selected at random. What is the probability that at least one has not received the recommended immunization?
To find the probability that at least one toddler has not received the recommended immunization, we can first find the probability that all six toddlers have received the immunization and then subtract it from 1.
The probability that a randomly selected toddler has received the immunization is 76%, which can be written as 0.76. Therefore, the probability that a randomly selected toddler has not received the immunization is 1 - 0.76 = 0.24.
Since the six toddlers are selected independently, the probability that all six have received the immunization is found by multiplying the individual probabilities together. We can calculate this as:
0.24^6 = 0.0000534
Finally, subtracting this probability from 1 will give us the probability that at least one toddler has not received the recommended immunization:
1 - 0.0000534 = 0.9999466
Therefore, the probability that at least one toddler has not received the recommended immunization is approximately 0.9999 or 99.99%.