You have a sample space of 2 events called A and B. From your experimental observations you determine the probability of A or B {i.e. P(A or B)} to be 71%. You also conclusively determine that the probability of A is 30% and the joint probability of both events occurring is 19%. What is P(B)
Eight people were asked how many immediate family members they have. The results were (5, 2, 4, 4, 3, 6, 7, 7). If one of the eight people were selected at random, what is the change of selecting an even number or less than 4
P(A∪B)=0.71
P(A)=0.3
P(A∩B)=0.19
The visual way to solve this problem is to draw a Venn diagram and fill in the respective probabilities.
If you prefer to solve it mathematically, use:
P(A∪B)=P(A)+P(B)-P(A∩B)
60
To find the probability of event B, we can use the formula P(B) = P(A or B) - P(A) + P(A and B).
We have been given that P(A or B) = 71% and P(A) = 30%. We also know that the joint probability of both events occurring, P(A and B), is 19%.
Using the formula, we can now calculate P(B):
P(B) = P(A or B) - P(A) + P(A and B)
P(B) = 71% - 30% + 19%
P(B) = 40% + 19%
P(B) = 59%
Therefore, the probability of event B (P(B)) is 59%.
Now let's move on to the second question:
To find the probability of selecting an even number or less than 4 from the given list of numbers (5, 2, 4, 4, 3, 6, 7, 7), we need to count the number of favorable outcomes and divide it by the total number of possible outcomes.
The favorable outcomes in this case are the numbers that are either even or less than 4: 2, 4, 4, 3.
Now, let's calculate the probability:
Total number of outcomes = 8 (since there are 8 people)
Number of favorable outcomes = 4 (since there are 4 numbers that are even or less than 4)
Probability = Number of favorable outcomes / Total number of outcomes
Probability = 4 / 8
Probability = 0.5 or 50%
Therefore, the probability of selecting an even number or less than 4, when choosing one of the eight people at random, is 50%.