Consider an experiment with four possible outcomes which we denote by Wi for i = 1,2,3,4. Sample space is Omega = {w1,w2,w3,w4}. Consider events A= {w1}, B = {w1,w2}, C = {w1,w2,w3} and D = {w2,w4}. Given that P(A) = 1/10, P(B) = 1/2, P(C) = 7/10, compute P(D)
To compute P(D), we need to find the probability of event D, denoted by P(D). Here's how you can calculate it:
1. We know that the sample space, Omega, consists of four possible outcomes: {w1, w2, w3, w4}.
2. Event D is defined as D = {w2, w4}, meaning it contains the outcomes w2 and w4.
3. To calculate P(D), we need to find the probability of event D occurring, which is the number of favorable outcomes divided by the total number of outcomes.
Now let's break down the steps to determine P(D):
Step 1: Identify the favorable outcomes for event D.
In this case, event D consists of outcomes w2 and w4. So, there are two favorable outcomes.
Step 2: Determine the total number of outcomes.
Since there are four possible outcomes in the sample space ({w1, w2, w3, w4}), the total number of outcomes is 4.
Step 3: Calculate P(D).
P(D) = (Number of favorable outcomes) / (Total number of outcomes)
P(D) = (2) / (4)
P(D) = 1/2
Therefore, the probability of event D (P(D)) is 1/2.