The probability of an event P is 3/4 while that of another event is 1/6. If the probability of both P and Q is 1/12 what is the probability of either P or Q.
well, recall that
P(P)+P(Q) - P(P&Q) = P(P or Q)
just think of a Venn diagram
To find the probability of either event P or event Q, you need to use the addition rule of probability.
The addition rule states that for two mutually exclusive events (events that cannot occur at the same time), the probability of either event occurring is the sum of their individual probabilities.
Let's denote the probability of event P as P(P) and the probability of event Q as P(Q).
Given:
P(P) = 3/4
P(Q) = 1/6
P(P and Q) (the probability of both P and Q occurring) = 1/12
To find the probability of either P or Q, you can use the formula:
P(P or Q) = P(P) + P(Q) - P(P and Q)
Substituting the given values:
P(P or Q) = 3/4 + 1/6 - 1/12
To evaluate this expression, you need to find a common denominator:
P(P or Q) = (9/12) + (2/12) - (1/12)
Combining the fractions:
P(P or Q) = 10/12
Finally, you can simplify this fraction:
P(P or Q) = 5/6
Therefore, the probability of either event P or event Q occurring is 5/6.
To find the probability of either event P or event Q, we can use the principle of inclusion-exclusion.
The probability of event P is 3/4, and the probability of event Q is 1/6. Let's denote the probability of either event P or event Q as P(P or Q).
Using the principle of inclusion-exclusion, we can calculate P(P or Q) as follows:
P(P or Q) = P(P) + P(Q) - P(P and Q),
where P(P) represents the probability of event P, P(Q) represents the probability of event Q, and P(P and Q) represents the probability of both event P and event Q occurring simultaneously.
Given that P(P) = 3/4, P(Q) = 1/6, and P(P and Q) = 1/12, we can substitute the values into the formula:
P(P or Q) = 3/4 + 1/6 - 1/12.
To simplify this expression and add the fractions, we need a common denominator. The least common denominator for 4, 6, and 12 is 12.
P(P or Q) = (9/12) + (2/12) - (1/12).
Combining the fractions:
P(P or Q) = (9 + 2 - 1) / 12.
P(P or Q) = 10 / 12.
To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 2:
P(P or Q) = 5 / 6.
Therefore, the probability of either event P or event Q occurring is 5/6.