Questions: A container contains 40 green tokens, 10 blue tokens, and 2 red tokens. Two tokens are randomly selected without replacement. Compute P(F E). E-you select a non-blue token first F - the second token is non - blue

Solution Steps

To find the probability of selecting a non-blue token first, we use the hypergeometric distribution. The total number of tokens is \( N = 52 \), and the number of non-blue tokens (green and red) is \( K = 42 \). The probability is calculated as follows:

\[ P(E) = \frac{\binom{K}{1} \binom{N-K}{0}}{\binom{N}{1}} = \frac{\binom{42}{1} \binom{10}{0}}{\binom{52}{1}} = 0.8077 \]

Next, we calculate the probability of selecting a non-blue token first and a non-blue token second. After selecting a non-blue token first, there are \( N - 1 = 51 \) tokens left, with \( K - 1 = 41 \) non-blue tokens remaining. The probability is given by:

\[ P(F \cap E) = \frac{\binom{K-1}{1} \binom{N-K}{0}}{\binom{N-1}{1}} = \frac{\binom{41}{1} \binom{10}{0}}{\binom{51}{1}} = 0.8039 \]

Finally, we compute the conditional probability \( P(F | E) \) using the formula:

\[ P(F | E) = \frac{P(F \cap E)}{P(E)} = \frac{0.8039}{0.8077} \approx 0.9953 \]

Final Answer