Understanding Complementary Events: Analyzing Probabilities of Different Pairs

Which pair does not represent the probabilities of complementary events?

To determine which pair does not represent the probabilities of complementary events, we need to understand what complementary events are

To determine which pair does not represent the probabilities of complementary events, we need to understand what complementary events are.

Complementary events are two events that together cover all possible outcomes of an experiment. The probability of an event happening, and the probability of its complement (the event not happening), should add up to 1.

Let’s consider four pairs of events, A and B, and calculate their respective probabilities:

Pair 1:
Event A: Rolling an even number on a fair six-sided die
Event B: Rolling an odd number on a fair six-sided die

The probability of event A: There are three even numbers (2, 4, and 6) out of six possible outcomes. So, the probability of rolling an even number is 3/6 or 1/2.

The probability of event B: There are three odd numbers (1, 3, and 5) out of six possible outcomes. So, the probability of rolling an odd number is also 3/6 or 1/2.

Since both events have a probability of 1/2, this pair represents complementary events.

Pair 2:
Event A: Flipping a fair coin and getting heads
Event B: Flipping a fair coin and getting tails

The probability of event A: In a fair coin flip, there are two possible outcomes, heads or tails. So the probability of getting heads is 1/2.

The probability of event B: Similarly, the probability of getting tails is also 1/2.

Since both events have a probability of 1/2, this pair represents complementary events as well.

Pair 3:
Event A: Choosing a red marble from a bag containing 5 red and 5 blue marbles
Event B: Choosing a blue marble from the same bag

The probability of event A: There are 5 red marbles out of 10 in total. So, the probability of choosing a red marble is 5/10 or 1/2.

The probability of event B: Similarly, there are 5 blue marbles out of 10 in total. So, the probability of choosing a blue marble is also 5/10 or 1/2.

Once again, both events have a probability of 1/2, making this pair represent complementary events.

Pair 4:
Event A: Drawing an ace from a standard deck of 52 cards
Event B: Drawing a king from the same deck

The probability of event A: There are four aces in a deck of 52 cards. So, the probability of drawing an ace is 4/52, which simplifies to 1/13.

The probability of event B: There are four kings in a deck of 52 cards as well. So, the probability of drawing a king is also 4/52 or 1/13.

Once again, both events have a probability of 1/13, indicating that this pair represents complementary events.

After analyzing all four pairs, we can conclude that there is no pair that does not represent the probabilities of complementary events.

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