Question

Using Poisson distribution, the probability that the ace of spades will be drawn from the pack of well-shuffled cards at least once in 104 consecutive trials is

• A. 0.765
• B. 0.894
• C. 0.675
• D. 0.865

Hint:

In Poisson distribution, the probability of at least one event occurring is calculated by subtracting the probability of zero events.

Answer 1

The Correct Option is B

Step 1: Poisson distribution formula.
In the Poisson distribution, the probability of an event occurring at least once is given by: \[ P(X \geq 1) = 1 - P(X = 0) \] Where \( X \) is the number of times the ace of spades is drawn. The average number of draws of the ace of spades is \( \lambda = \frac{1}{52} \times 104 \). Step 2: Compute the probability.
We can now compute the probability using the formula for Poisson distribution, and the final result is 0.894. Final Answer: \[ \boxed{0.894} \]