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Math  /  Data & Statistics

QuestionConsider the following binomial probability distribution expression below. The number of trials, the number of successes, the probability of success and the probability of failure respectively are: (127)(0.1)7(0.9)5\binom{12}{7}(0.1)^{7}(0.9)^{5} 7,0.1,0.9,127,0.1,0.9,12 12,7,0.1,0.912,7,0.1,0.9 12,7,0.9,0.112,7,0.9,0.1 7,0.9,12,0.17,0.9,12,0.1

Studdy Solution

STEP 1

1. The expression given is a binomial probability expression.
2. The binomial probability formula is given by: $ P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} \] where \( n \) is the number of trials, \( k \) is the number of successes, \( p \) is the probability of success, and \( 1-p \) is the probability of failure.

STEP 2

1. Identify the components of the binomial expression.
2. Match the components to the correct option.

STEP 3

Identify the components from the expression (127)(0.1)7(0.9)5\binom{12}{7}(0.1)^{7}(0.9)^{5}:
- Number of trials n=12 n = 12 - Number of successes k=7 k = 7 - Probability of success p=0.1 p = 0.1 - Probability of failure 1−p=0.9 1-p = 0.9

STEP 4

Match the identified components to the correct option:
- Number of trials n=12 n = 12 - Number of successes k=7 k = 7 - Probability of success p=0.1 p = 0.1 - Probability of failure 1−p=0.9 1-p = 0.9
The correct option is: 12,7,0.1,0.9 12, 7, 0.1, 0.9
The correct answer is:
12,7,0.1,0.9 \boxed{12, 7, 0.1, 0.9}

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