Question

# Fifty-seven percent of families say that their children have an influence on their vacation plans. Consider...

Fifty-seven percent of families say that their children have an influence on their vacation plans. Consider a sample of eight families who are asked if their children influence their vacation plans. What is the probability that exactly three families say that their children have an influence on their vacation plans.

Using the above problem, how many failures are there?

The probability that a randomly selected family say that their children have an influence on their vacation plans = 0.57

Let X denotes the number of families who are asked if their children influence their vacation plans in a random sample of 8 families.

Here,

X ~ Binomial(n = 8, p = 0.57)

The probability mass function of X is

Now,

The probability that exactly three families say that their children have an influence on their vacation plans is

Assuming that finding a family who say that their children have an influence on their vacation plans as success,

number of failures =trial size (n) - number of successes = 8 - 3 = 5

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