# Without Replacement Question Statistics Question Need Help *Trying To Make Sick Dad Proud*?

Five cards are drawn at random from a deck. Here a deck contains 52 cards

in total, in which four are Ace.

1) If the cards are drawn without replacement, then what is the probability that the first

card is an Ace, and the second card is not an Ace?

A 0.0769 B 0.0724 C 0.0710 D 0.0045

(ANSWER WAS B) I need steps as to how

2) 7. If these cards are drawn without replacement, can you guess the mean value of the

number of Ace cards selected?

A 0.3846 B 0.3077 C 0.0769 D 1.5385

ANSWER WAS A I NEED HELP WITH STEPS AS TO HOW

Relevance
• 3 years ago

1) P(first card drawn is an ace) = P(A) = 4/52

P(second card drawn is not an ace) = P(B/A) = 48/51

Since the events A and B are dependent, according to the Multiplication Theorem of Probability

P(A and B) = P(A) * P(B/A)

Therefore, Required probability = 4/52 * 48/51 = 0.0724

2) Probability distribution of X (the number of ace cards drawn)

X ----- P(X)

0 ----- 4C0*48C5/52C5 = 0.6588

1 ----- 4C1*48C4/52C5 = 0.2995

2 ----- 4C2*48C3/52C5 = 0.0400

3 ----- 4C3*48C2/52C5 = 0.0017

4 ----- 4C4*48C1/52C5 = 0.0000

Total ------------------------ = 1.0000

Mean = sigma x*p

= [0*0.6588] + [1*0.2995] + [2*0.400] + [3*0.0017] + [4*0.0000]

= 0.3846