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The problem involves calculating the probability that fewer than 3 out of 6 randomly selected consumers believe that cash will become obsolete in the next 20 years. Given that 40.3% of consumers believe this, we can use the binomial probability formula:

The formula for the binomial probability is:
\[
P(X = k) = \binom{n}{k} p^k (1 - p)^{n - k}
\]

where:
- \( n \) = 6 (number of trials)
- \( p \) = 0.403 (probability of success, where success is defined as a consumer believing cash will be obsolete)
- \( k \) = number of successes (0, 1, or 2 since we are looking for "fewer than 3")

To find the probability that fewer than 3 consumers believe cash will be obsolete, we need to calculate \( P(X < 3) \), which means summing up the probabilities for \( X = 0 \), \( X = 1 \), and \( X = 2 \).

Let’s calculate these probabilities:

1. **For \( X = 0 \)**:
   \[
   P(X = 0) = \binom{6}{0} \cdot 0.403^0 \cdot (1 - 0.403)^6
   \]

2. **For \( X = 1 \)**:
   \[
   P(X = 1) = \binom{6}{1} \cdot 0.403^1 \cdot (1 - 0.403)^5
   \]

3. **For \( X = 2 \)**:
   \[
   P(X = 2) = \binom{6}{2} \cdot 0.403^2 \cdot (1 - 0.403)^4
   \]

After calculating each term, sum them to get the total probability \( P(X < 3) \).

Would you like a detailed step-by-step calculation for each term?

40.3% of consumers believe that cash will be obsolete in the next 20 years. Assume that 6 consumers are randomly selected. Find the probability that fewer than 3 of the selected consumers believe that cash will be obsolete in the next 20 years. Round to three decimal places as needed.

Calculate the probability that fewer than 3 out of 6 randomly selected consumers believe that cash will become obsolete in the next 20 years. Learn how to apply the binomial probability formula with 40.3% belief rate. Includes step-by-step instructions and rounding to three decimal places.

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