Question

Two cards are chosen at random without replacement from a pack of 52 playing cards if the first card chosen is an Ace what is the probability the second card chosen is also an ace

Answer 1

So originally you have 52 cards which means that no matter what card you want it'll be a 1/52 chance pulling that exact card.

You pull an Ace which gives you 51 cards left, and a 1/51 chance of pulling the card you want.

You want another Ace, and since it's a full deck of cards means that there should be 3 Aces left in the deck.

Probability of pulling another Ace is 3/51. Hope this Helps.

Answer 2

The probability of drawing both aces without replacement is thus 4/52*3/51, or approximately .005.

What is Probability ?

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur.

The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty.

Probability Formula = f/n

where,

f is the number of times an event occurs

n is the total number of trials

In the question it is given that  there are 52 cards

Probabilty that first card is an ace  = 4/52

After taking out an Ace 51 cards are left,

You want another Ace, and 3 Ace will be left in the deck .

Probability of pulling another Ace is 3/51.

The probability of two consecutive draws without replacement from a deck of cards is calculated as the number of possible successes over the number of possible outcomes, multiplied together for each case.

Thus, for the first ace, there is a 4/52 probability and for the second there is a 3/51 probability.

The probability of drawing both aces without replacement is thus 4/52*3/51, or approximately .005.

To know more about Probability

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