John is playing a game with a standard deck of playing cards. He wants to draw a jack on the first try. Which of the following statements is true?

a. The probability that John draws a jack on the first try is 1/13. If John replaces the card, re- shuffles, and draws again, the probability that he will pull another jack increases.
b. The probability that John draws a jack on the first try is 3/13. If John replaces the card, re- shuffles, and draws again, the probability that he will pull another jack stays the same.
c. The probability that John draws a jack on the first try is 1/13. If John replaces the card, re- shuffles, and draws again, the probability that he will pull another jack decreases.
d. The probability that John draws a jack on the first try is 1/13. If John replaces the card, re- shuffles, and draws again, the probability that he will pull another jack stays the same.

The probability that John draws a jack on the first try is 1/13. If John replaces the card, re-shuffles, and draws again, the probability that he will pull another jack stays the same. Hence, statement d is correct.

What do we mean by the probability of an event?

The probability of an event is the ratio of the number of favorable outcomes to the event to the total number of outcomes for the experiment.

If we have an event A, the number of favorable outcomes to event A is n, and the total number of outcomes in the experiment is S, then the probability of the event A is given by,

P(A) = n/S.

How do we solve the given question?

We are given that John is playing a game with a standard deck of playing cards.

We are said that he wants to try to draw a jack on the first try.

Let the event of drawing a jack be A.

The number of outcomes favorable to the event A (n) = 4 (number of jacks)

The total number of outcomes in the experiment of drawing a card (S) = 52 (the total number of cards)

∴ The probability of the event A is given by,

P(A) = n/S = 4/52 = 1/13.

∴ The probability of drawing a jack on the first try is 1/13.

When he replaces the card and re-shuffles it, the probability will be the same as the number of favorable outcomes and the total number of outcomes remains the same.

∴ The probability that John draws a jack on the first try is 1/13. If John replaces the card, re-shuffles, and draws again, the probability that he will pull another jack stays the same. Hence, statement d is correct.

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