To solve this problem, we can model it as a binomial distribution. In a binomial distribution, the probability of success (getting an interview) is $p = 0.2$, and the probability of failure (not getting an interview) is $1 - p = 0.8$. You are applying for 5 jobs, so the number of trials is $n = 5$.

We need to find the probability of getting less than two interviews, which means getting either 0 or 1 interview. This is the sum of the probabilities for 0 interviews and 1 interview.

The probability mass function (PMF) of a binomial distribution 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 (in this case, the number of interviews),
• $p$ is the probability of success,
• $\binom{n}{k}$ is the binomial coefficient, representing the number of ways to choose $k$ successes from $n$ trials.

We need to calculate $P(X = 0)$ and $P(X = 1)$, then add them together.

Step 1: Probability of 0 interviews $(X = 0)$

$P(X = 0) = \binom{5}{0} (0.2)^0 (0.8)^5 = 1 \cdot 1 \cdot (0.8)^5 = 0.32768$

Step 2: Probability of 1 interview $(X = 1)$

$P(X = 1) = \binom{5}{1} (0.2)^1 (0.8)^4 = 5 \cdot 0.2 \cdot (0.8)^4 = 5 \cdot 0.2 \cdot 0.4096 = 0.4096$

Step 3: Total probability

Now, we sum these probabilities to find the probability of getting less than two interviews:

$P(X < 2) = P(X = 0) + P(X = 1) = 0.32768 + 0.4096 = 0.73728$

Thus, the probability of getting less than two interviews is approximately 0.737 or 73.7%.

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Would you like further details or have any questions?

Here are 5 follow-up questions you might find interesting:

1. What is the probability of getting exactly 2 interviews?
2. How would the probability change if you applied for 10 jobs instead of 5?
3. What is the expected number of interviews when applying for 5 jobs?
4. How would the calculation change if the probability of an interview were 30% instead of 20%?
5. Can we find the probability of getting at least one interview?

Tip: The binomial distribution is often used to model the number of successes in a fixed number of independent trials, such as flipping a coin or applying for jobs.