We are interested in the probability that all five women dislike their mother-in-law. Therefore, we want to find the probability of five successes, or Pr = .

To find the probability that all five women dislike their mother-in-law, we need to define a few parameters and utilize the binomial probability formula. Here are the steps to compute the desired probability:

1. Break Down the Problem

We identify two important factors:

• $n$: the total number of trials (women in this case).
• $p$: the probability of success, which is the probability that a woman dislikes her mother-in-law.

2. Relevant Concepts

The binomial probability formula is given by:

$P(X = k) = \binom{n}{k} p^k (1-p)^{n-k}$

Where:

• $\binom{n}{k}$ is the binomial coefficient, which represents the number of ways to choose $k$ successes from $n$ trials.
• $k$: the number of successes (in this case, $k = 5$).
• $n$: the number of trials (in this case, $n = 5$).
• $p$: probability of success (the probability that one woman dislikes her mother-in-law).
• $(1 - p)$: probability of failure (the probability that one woman likes her mother-in-law).

3. Analysis and Detail

To find $Pr$ for all five women disliking their mother-in-law, we set $k = 5$ and $n = 5$:

$P(X = 5) = \binom{5}{5} p^5 (1-p)^{5-5}$

The binomial coefficient $\binom{5}{5} = 1$, so:

$P(X = 5) = 1 \cdot p^5 \cdot (1-p)^0$

This simplifies to:

$P(X = 5) = p^5$

Here, $p$ must be determined from context. If the probability $p$ is known, this expression allows us to calculate $Pr$.

4. Verify and Summarize

Now you need to plug in the specific value for $p$ to get the final answer. Ensure that the value is between 0 and 1, as it represents a probability.

Final Answer

Thus, the probability of all five women disliking their mother-in-law is given by:

$P(X = 5) = p^5$

If you provide the value of $p$, we can compute the exact numeric probability.