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.
The probability of observing an event at least once in a Poisson distribution is calculated as:\[P(X \geq 1) = 1 - P(X = 0)\]Here, \( X \) represents the number of times the ace of spades appears, and the average number of ace of spades draws is \( \lambda = \frac{1}{52} \times 104 \).Step 2: Compute the probability.
Using the Poisson distribution formula, we calculate the probability, which equals 0.894. Final Answer: \[ \boxed{0.894} \]