Answer:
A) 1/2197
B) 1/5525
Explanation:
Probability is the likelihood or chance that an event will occur.
Probability = Expected outcome/Total outcome.
Since there are 52 random cards in a deck of card, the total outcome will be 52.
a) Also in a deck of card, there are 4 aces. If we are to select 3 aces with replacement, this means that each time we pick up an ace from the card, it was returned.
Pr(drawing an ace) = 4/52
Pr(drawing 3 aces and replacing it) = 4/52 *4/52*4/52
Pr(drawing 3 aces and replacing it) = 64/140,608
Pr(drawing 3 aces and replacing it) = 1/2197
b) If we pick 3 aces without replacement then each time we pick an ace, the total number cards keeps reducing.
Pr(picking the first ace) = 4/52
Pr(picking the second ace without replacing) = 3/51 (Since we didn't replace the first one, the total ace in the deck of card will reduce to 3 and the total will be 51)
Pr(picking the third ace without replacing) = 2/50 (since we didn't replace the first two aces, the total ace in the deck of card will reduce to 2 and the total will be 50)
Pr(drawing 3 aces without replacement) = 4/52*3/51*2/50
Pr(drawing 3 aces without replacement) = 24/132,600
Pr(drawing 3 aces without replacement) = 1/5525