Is the following situation a dependent event or an independent event? *
Tom chooses a letter of the alphabet, then Beth must choose a different letter from the alphabet.
is the following situation independent ?
Yes.
The given situation is a dependent event.
To understand why, we need to consider the definition of dependent and independent events.
In an independent event, the outcome of one event does not affect the outcome of the other event. Each event occurs with its own probability, completely unrelated to the other event. For example, tossing a coin twice, where the outcome of the first toss does not influence the outcome of the second toss, is an independent event.
On the other hand, in a dependent event, the outcome of one event does affect the outcome of the other event. The probability of the second event is dependent on the outcome of the first event. For example, drawing cards from a deck without replacement, where the probability of drawing a certain card changes after each draw, is a dependent event.
In the given situation, Tom chooses a letter of the alphabet, and then Beth must choose a different letter from the alphabet. The outcome of Beth's choice is directly dependent on the choice made by Tom. If Tom chooses the letter "A," Beth no longer has the option to choose that same letter. So, the probability of Beth choosing a specific letter changes based on what letter Tom selected.