In a game, a woman wins 16 times out of 20 balls she p lays. Find the probability that she does not win the game.

Answer

To find the probability that the woman does not win the game, we can follow these steps:

### Step 1: Identify the number of wins and total games played.
The woman wins 16 times out of 20 balls played.

### Step 2: Calculate the probability of winning.
The probability of winning (P(win)) can be calculated using the formula:
\[ P(\text{win}) = \frac{\text{Number of wins}}{\text{Total games played}} \]
Substituting the values:
\[ P(\text{win}) = \frac{16}{20} \]

### Step 3: Simplify the probability of winning.
To simplify \( \frac{16}{20} \):
\[ P(\text{win}) = \frac{16 \div 4}{20 \div 4} = \frac{4}{5} \]

### Step 4: Calculate the probability of not winning.
The probability of not winning (P(not win)) can be found using the relationship:
\[ P(\text{not win}) = 1 - P(\text{win}) \]
Substituting the value we found:
\[ P(\text{not win}) = 1 - \frac{4}{5} \]

### Step 5: Simplify the probability of not winning.
Calculating this gives:
\[ P(\text{not win}) = \frac{5}{5} - \frac{4}{5} = \frac{1}{5} \]

### Final Answer:
The probability that the woman does not win the game is \( \frac{1}{5} \).

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