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= [tex]\frac{3}{4}[/tex]×[tex]\frac{3}{4}[/tex]
=[tex]\frac{9}{16}[/tex]
Thus, Probability that at least one of the two cards was a heart= 1- P( Neither of two cards had a heart= 1- [tex]\frac{9}{16}[/tex]
=[tex]\frac{7}{16}[/tex]
Second way:
Probability that first card drawn is a heart and the second one is not a heart= [tex]\frac{1}{4}[/tex]×[tex]\frac{3}{4}[/tex]
=[tex]\frac{3}{16}[/tex]
Probability that the first card drawn is not a heart and the second one is a heart= [tex]\frac{3}{4}[/tex]×[tex]\frac{1}{4}[/tex]
=[tex]\frac{3}{16}[/tex]
Probability that both cards drawn are hearts= [tex]\frac{1}{4}[/tex]×[tex]\frac{1}{4}[/tex]
=[tex]\frac{1}{16}[/tex]
Adding all these probabilities, we have the probability that at least one of the card drawn was heart= [tex]\frac{7}{16}[/tex]
