Question

A street magician asks a passerby to draw one card from a standard deck, remember it, and then replace it. The magician then shuffles the deck and asks the person to draw a second card. Find the probability that at least one of the two cards was a heart.

Answer 1

Answer:

P( At least one of the two cards was a heart)=7/16

Step-by-step explanation:

The solution to this question can be found in two ways.

First way: Since total number of heart in a deck are four,

Probability that neither of two cards had a heart is that at both times the card drawn was not a heart, since it is an independent event, thus probability both were not heart= $\frac{3}{4}$×$\frac{3}{4}$

=$\frac{9}{16}$

Thus, Probability that at least one of the two cards was a heart= 1- P( Neither of two cards had a heart= 1- $\frac{9}{16}$

=$\frac{7}{16}$

Second way:

Probability that first card drawn is a heart and the second one is not a heart= $\frac{1}{4}$×$\frac{3}{4}$

=$\frac{3}{16}$

Probability that the first card drawn is not a heart and the second one is a heart= $\frac{3}{4}$×$\frac{1}{4}$

=$\frac{3}{16}$

Probability that both cards drawn are hearts= $\frac{1}{4}$×$\frac{1}{4}$

=$\frac{1}{16}$

Adding all these probabilities, we have the probability that at least one of the card drawn was heart= $\frac{7}{16}$