In a binomial experiment, if there are two possible outcomes and [tex]P(S)=0.36$[/tex], what is [tex]P(F)$[/tex]?
A. 0.06
B. 0.74
C. 0.36
D. 0.64
Answer (1)
The problem states that in a binomial experiment, P ( S ) = 0.36 and asks to find P ( F ) .
The probabilities of success and failure must sum to 1: P ( S ) + P ( F ) = 1 .
Substitute the given value: 0.36 + P ( F ) = 1 .
Solve for P ( F ) : P ( F ) = 1 − 0.36 = \boxed{{0.64}}$
Explanation
Understand the problem In a binomial experiment, there are only two possible outcomes: success (S) or failure (F). The probabilities of these two outcomes must add up to 1. We are given that the probability of success, P ( S ) , is 0.36. We need to find the probability of failure, P ( F ) .
Set up the equation Since the sum of the probabilities of success and failure must equal 1, we can write the equation: P ( S ) + P ( F ) = 1
Substitute the given value We are given P ( S ) = 0.36 . Substitute this value into the equation: 0.36 + P ( F ) = 1
Isolate P(F) To solve for P ( F ) , subtract 0.36 from both sides of the equation: P ( F ) = 1 − 0.36
Calculate P(F) Calculate the value of P ( F ) :
P ( F ) = 0.64
State the final answer Therefore, the probability of failure, P ( F ) , is 0.64.
Examples
Consider a simple scenario: flipping a biased coin. If the probability of getting heads (success) is 0.36, then the probability of getting tails (failure) is 0.64. This concept is widely used in quality control, where items are tested for defects. If the probability of an item being defective is known, we can easily find the probability of it being non-defective.
