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

7/16

Explanation:

dont need a explanation.

dummy lit

Answer 2

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

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=
`(3)/(4)`×
`(3)/(4)`

=
`(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-
`(9)/(16)`

=
`(7)/(16)`

Second way:

Probability that first card drawn is a heart and the second one is not a heart=
`(1)/(4)`×
`(3)/(4)`

=
`(3)/(16)`

Probability that the first card drawn is not a heart and the second one is a heart=
`(3)/(4)`×
`(1)/(4)`

=
`(3)/(16)`

Probability that both cards drawn are hearts=
`(1)/(4)`×
`(1)/(4)`

=
`(1)/(16)`

Adding all these probabilities, we have the probability that at least one of the card drawn was heart=
`(7)/(16)`