What is the probability that a baby will be born on a Friday OR a Saturday OR a Sunday if all the days of the week are equally likely as birthdays?
The Correct Answer and Explanation is :
To solve this problem, we need to calculate the probability that a baby will be born on one of three days: Friday, Saturday, or Sunday, assuming that all days of the week are equally likely as birthdays.
Step-by-Step Explanation:
- Understanding the probability for each day:
There are 7 days in a week (Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday). If the baby’s birthday is equally likely to fall on any of these days, the probability of being born on any one specific day is: [
P(\text{specific day}) = \frac{1}{7}
] - Identifying the days we are interested in:
We are interested in the probability of the baby being born on either Friday, Saturday, or Sunday. Since these are three specific days, we can add up their individual probabilities. - Calculating the combined probability:
Since the events (being born on Friday, Saturday, or Sunday) are mutually exclusive (the baby can’t be born on more than one day at once), we can simply sum the individual probabilities for these three days: [
P(\text{Friday OR Saturday OR Sunday}) = P(\text{Friday}) + P(\text{Saturday}) + P(\text{Sunday})
] Using the probability for each specific day (which is ( \frac{1}{7} )): [
P(\text{Friday OR Saturday OR Sunday}) = \frac{1}{7} + \frac{1}{7} + \frac{1}{7} = \frac{3}{7}
]
Final Answer:
The probability that a baby will be born on a Friday, Saturday, or Sunday is ( \frac{3}{7} ).
Explanation:
This problem assumes that each day of the week is equally likely to be the birthday, so the probability for each day is ( \frac{1}{7} ). By adding up the probabilities for the three days (Friday, Saturday, and Sunday), we find that the total probability is ( \frac{3}{7} ). This approach is a straightforward application of the addition rule of probability for mutually exclusive events.