Question

a card is chosen at random from a standard deck of 52 playing cards. Without replacing it, a second card is choose . what is a queen probability that the first card chosen is a queen and the second is a jack

Answer 1

Hey!

Experiment 1: A card is chosen at random from a standard deck of 52 playing cards. Without replacing it, a second card is chosen. What is the probability that the first card chosen is a queen and the second card chosen is a jack?

Analysis: The probability that the first card is a queen is 4 out of 52. However, if the first card is not replaced, then the second card is chosen from only 51 cards. Accordingly, the probability that the second card is a jack given that the first card is a queen is 4 out of 51.

Conclusion: The outcome of choosing the first card has affected the outcome of choosing the second card, making these events dependent.

Definition: Two events are dependent if the outcome or occurrence of the first affects the outcome or occurrence of the second so that the probability is changed.

Now that we have accounted for the fact that there is no replacement, we can find the probability of the dependent events in Experiment 1 by multiplying the probabilities of each event. Experiment 1: A card is chosen at random from a standard deck of 52 playing cards. Without replacing it, a second card is chosen. What is the probability that the first card chosen is a queen and the second card chosen is a jack?

Probabilities:

P(queen on first pick) =  4 52 P(jack on 2nd pick given queen on 1st pick) =  4 51 P(queen and jack) =  4  ·  4  =   16   =   4  52512652663

Experiment 1 involved two compound, dependent events. The probability of choosing a jack on the second pick given that a queen was chosen on the first pick is called a conditional probability.

Hope this helps! ~Nadia~