Out of five siblings, what is the probability that the eldest and youngest children have the same gender?
Out of five siblings, what is the probability that the eldest and youngest children have the same gender?
Solution and Explanation
To determine the probability that the eldest and youngest children have the same gender among five siblings, we need to consider the possible combinations of genders for the eldest and youngest children.
For each child, there are two possible genders: male (M) or female (F). Therefore, the total number of possible gender combinations for the eldest and youngest children is 2^2 = 4.
Let's examine each possible combination:
- MM: The eldest and youngest are both male.
- FF: The eldest and youngest are both female.
- MF: The eldest is male and the youngest is female.
- FM: The eldest is female and the youngest is male.
Out of these four combinations, two have the same gender for the eldest and youngest children (MM and FF).
Therefore, the probability that the eldest and youngest children have the same gender is 2/4 = 1/2, which can also be expressed as 0.5 or 50%.
So, there is a 50% chance that the eldest and youngest children have the same gender among the five siblings.
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Concepts Used:
Probability
Probability is defined as the extent to which an event is likely to happen. It is measured by the ratio of the favorable outcome to the total number of possible outcomes.
The definitions of some important terms related to probability are given below:
Sample space
The set of possible results or outcomes in a trial is referred to as the sample space. For instance, when we flip a coin, the possible outcomes are heads or tails. On the other hand, when we roll a single die, the possible outcomes are 1, 2, 3, 4, 5, 6.
Sample point
In a sample space, a sample point is one of the possible results. For instance, when using a deck of cards, as an outcome, a sample point would be the ace of spades or the queen of hearts.
Experiment
When the results of a series of actions are always uncertain, this is referred to as a trial or an experiment. For Instance, choosing a card from a deck, tossing a coin, or rolling a die, the results are uncertain.
Event
An event is a single outcome that happens as a result of a trial or experiment. For instance, getting a three on a die or an eight of clubs when selecting a card from a deck are happenings of certain events.
Outcome
A possible outcome of a trial or experiment is referred to as a result of an outcome. For instance, tossing a coin could result in heads or tails. Here the possible outcomes are heads or tails. While the possible outcomes of dice thrown are 1, 2, 3, 4, 5, or 6.