If P(C) = 0.2, P(D) = 0.3, and P(C | D) = 0.4 find P(C and D).
To find P(C and D), we can use the formula for conditional probability:
P(C and D) = P(C | D) * P(D)
Given:
P(C) = 0.2
P(D) = 0.3
P(C | D) = 0.4
Using the formula, substituting the given values:
P(C and D) = 0.4 * 0.3
P(C and D) = 0.12
Therefore, P(C and D) is equal to 0.12.
To find the probability of both events C and D happening (P(C and D)), you can use the formula:
P(C and D) = P(C | D) * P(D)
Given that P(C | D) = 0.4 and P(D) = 0.3, you can substitute these values into the formula:
P(C and D) = 0.4 * 0.3
Calculating this expression, you get:
P(C and D) = 0.12
Therefore, the probability of both events C and D happening is 0.12 or 12%.
To find P(C and D), you can use the formula for conditional probability:
P(C and D) = P(C | D) * P(D)
Given that P(C | D) = 0.4 and P(D) = 0.3, you can substitute these values into the formula:
P(C and D) = 0.4 * 0.3
Multiply 0.4 by 0.3 to get the answer:
P(C and D) = 0.12
Therefore, the probability of both C and D occurring, P(C and D), is 0.12.