Cards are drawn one at a time from a full deck of 52 cards. Between drawings, th
ID: 2932958 • Letter: C
Question
Cards are drawn one at a time from a full deck of 52 cards. Between drawings, the drawn card is placed back into the deck and shuffled before the next card is drawn.
What is the probability that the Ace of Spades is drawn exactly ONCE in 10 drawings?
What is the probability that the Ace of Spades is drawn exactly FIVE TIMES in 10 drawings
What is the probability that the Ace of Spades is NOT drawn after 20 drawings?
What is the expected number (ie mean) of drawings needed before the Ace of Spades is first drawn?
Explanation / Answer
Solution- 1. Let us denote the number of ace of Spades drawn by X which follows binomial distribution with parameters
number of trials ( n) = 10 and probability of success (p) = 1/52
required probability = P(X=1) = 10c1 * (1/52)^1 * (51/52)^9
= .1615
2. Let us denote the number of ace of Spades drawn by X which follows binomial distribution with parameters
number of trials ( n) = 10 and probability of success (p) = 1/52
required probability = P(X=5) = 10c5 * (1/52)^5 * (51/52)^5
= .0000006014
3. Let us denote the number of ace of Spades drawn by X which follows binomial distribution with parameters
number of trials ( n) = 20 and probability of success (p) = 1/52
required probability = 1 - P(X=0)
= 1 - .6781
= .3218
4. Let us denote the number of trials at which first Ace of Spades is drawn by X which follows negative binomial distribution with parameters
k = 1 and probability of success (p) = 1/52
the expected number (ie mean) of drawings needed before the Ace of Spades is first drawn = 1/(1/52)
= 52
Answers
TY!