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= \(\frac{7}{16}\)
