Suppose 20% of babies born are born early, 50% are born on time, and 30% are born late. A nurse uses a random-number table to find the experimental probability that of 5 births, at least 1 baby will be born early. The digits 0 and I represent babies born early. The digits 2, 3, 4, 5, and 6 represent babies born on time. The digits 7, 8, and 9 represent babies born late.
To find the probability of at least 1 baby being born early, we need to find the probability of none of the babies being born early and subtract it from 1. The probability of a baby not being born early is 80%, or 0, 2, 3, 4, 5, 6, 7, 8, or 9 on the table. So, the probability of none of the 5 babies being born early is:
0.8 x 0.8 x 0.8 x 0.8 x 0.8 = 0.32768
Therefore, the probability of at least 1 baby being born early is:
1 - 0.32768 = 0.67232 or 67.232% (rounded to the nearest thousandth)
To find the experimental probability that at least one baby will be born early, we need to find the probability of the complement event (i.e., no baby is born early) and subtract it from 1.
The nurse uses a random-number table, so we will simulate the births using the random digits.
Let's go step-by-step to determine the probability:
Step 1: Determine the probability of no baby being born early (complement event).
The digits 2, 3, 4, 5, and 6 represent babies born on time, which is 50% of the births. Thus, the probability of a baby being born on time is 0.5.
The digits 7, 8, and 9 represent babies born late, which is 30% of the births. Thus, the probability of a baby being born late is 0.3.
Since there are no digits representing babies born early, the probability of no baby being born early is 0.5+0.3 = 0.8 (as 80% of the births are not born early).
Step 2: Determine the probability of at least one baby being born early.
The probability of at least one baby being born early is equal to 1 minus the probability of no baby being born early.
So, P(at least one baby born early) = 1 - P(no baby being born early)
= 1 - 0.8
Step 3: Calculate the probability.
P(at least one baby born early) = 1 - 0.8 = 0.2
Therefore, the experimental probability that, out of 5 births, at least 1 baby will be born early is 0.2