According to the Central Statistics Office (CSO) there were 65 909 babies born in Ireland in 2015 - Leaving Cert Mathematics - Question 1 - 2017

The probability $P(B)$ that a randomly selected baby is a boy can be calculated using the formula:

$P(B) = \frac{\text{Number of boys}}{\text{Total number of babies}}$

Substituting the values:

$P(B) = \frac{33,619}{65,909} \approx 0.51$

Thus, the probability is approximately 0.51 when rounded to 2 decimal places.

The probability that the first three babies born were boys can be found by raising the probability of a boy to the power of 3:

$P(3 \text{ boys}) = (0.51)^3 \approx 0.132651$

Thus, the probability is approximately 0.1327 when rounded to 4 decimal places.

To find this probability, we consider that the first two births must be boys and the third must be a girl. This is calculated as:

$P(2 \text{ boys, 1 girl}) = (0.51)(0.51)(1-0.51) = (0.51)^2(0.49) \approx 0.127449$

Thus, the probability is approximately 0.1275 when rounded to 4 decimal places.

To complete the table, we need to ensure that the sum of probabilities equals 1. Adding the given probabilities:

$0.14 + 0.15 + 0.18 + 0.15 + 0.12 + 0.1 = 0.84$

Thus, the probability for Sunday is:

$1 - 0.84 = 0.16$

The completed table will include Sunday with a probability of 0.16.

To find the expected number of babies born on Tuesday, multiply the total number of babies born by the probability for Tuesday:

$Expected = 1300 \times 0.15 = 195$

Therefore, the expected number of babies born on Tuesday is 195.