Compound Events Portfolio

Answer 1

In the world of statistics and probability, compound events refer to a combination of two or more events occurring simultaneously. These events are often complex and require careful analysis to determine the likely outcomes. In this portfolio, we will explore various compound events and demonstrate how to calculate their probabilities.

1. Rolling Two Dice:

One of the classic examples of compound events is rolling two dice and determining the probability of getting a specific sum. There are a total of 36 possible outcomes when rolling two dice (6 possible outcomes for each die), and each outcome is equally likely. To calculate the probability of getting a sum of 5, for example, we need to determine the number of favorable outcomes and divide by the total number of outcomes.

Favorable outcomes for sum of 5: (1, 4), (2, 3), (3, 2), (4, 1)

Therefore, the probability of getting a sum of 5 when rolling two dice is 4/36 or approximately 0.1111.

2. Drawing Cards from a Deck:

Another common example of compound events is drawing cards from a deck and calculating the probability of getting specific combinations. For instance, if we want to find the probability of drawing two red cards in a row without replacement from a standard deck of 52 cards (26 red cards and 26 black cards), we need to consider the outcomes for each draw.

First draw: Probability of drawing a red card = 26/52 = 1/2
Second draw (without replacement): Probability of drawing another red card = 25/51

Therefore, the overall probability of drawing two red cards in a row is (1/2) * (25/51) = 25/102 or approximately 0.2451.

3. Tossing Coins:

Tossing multiple coins is another example of compound events. Suppose we toss three fair coins simultaneously, and we want to find the probability of getting exactly two heads. To calculate this probability, we need to consider the possible outcomes for each coin toss.

Possible outcomes for three coin tosses: HHH, HHT, HTH, THH, HTT, THT, TTH, TTT

There are 3 favorable outcomes (HHT, HTH, THH) out of 8 total outcomes. Therefore, the probability of getting exactly two heads when tossing three coins is 3/8 or approximately 0.375.

In conclusion, compound events are essential in understanding the probabilities of complex scenarios involving multiple outcomes. By carefully analyzing the possible outcomes and calculating their probabilities, we can make informed decisions and predict likely results in various situations.