Question

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

Answer 1

Given:

Trials = n = 104

To Find:

Probability that the ace of spades will be drawn using Poisson distribution

Solution:

Total number of cards in a deck = 52

Thus,

P ( Ace of spade) = p = 1/52

Number of trials = n = 104

Mean of Poisson distribution

= λ = m = n x p

= 104 x 1/52

= 2

The general form of Poisson distribution for determining the probability of r successes is

P(r) = e`-m x m`r / r!

Putting the values

e`-m = e`-2

= 0.13534

Required probability will be = P (r = at least once)

= 1 - P (r=0)

= 1 - e`-2 x 2`0 / 0!

= 1 - 0.13534 x 1 / 1

= 1 - 0.13534

= 0.86466

Answer: The probability is 86.466%