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Sagot :
The card deck is a standard deck of 52 cards, with 13 cards in each suit.
For the experiment carried out by Michelle, we have the following information:
n(Spades) = 9
n(Hearts) = 11
n(Clubs) = 7
n(Diamonds) = 3
The total number of times she performed the experiment is
[tex]n(\text{Total) = 9+11+7+3 = 30}[/tex]The empirical probability will make use of the experimental results, while the theoretical probability will make use of the total possibilities.
PART A: Empirical Probability of selecting a heart.
Probability is calculated by
[tex]P(\text{outcome) = }\frac{n(outcome)}{n(total)}[/tex]Therefore, the probability is calculated as
[tex]P(\text{heart) = }\frac{11}{30}[/tex]PART B: Theoretical probability of selecting a heart.
This is calculated by
[tex]\begin{gathered} P(\text{heart) = }\frac{13}{52} \\ P(\text{heart) = }\frac{1}{4} \end{gathered}[/tex]PART C: Empirical probability of selecting a club or diamond.
To calculate the probability for two outcomes, A or B, the probability can be calculated by
[tex]P(A\text{ or B) = P(A) + P(B)}[/tex]Therefore, we will find the probability of getting a club and then a diamond.
[tex]P(\text{heart) = }\frac{11}{30}[/tex][tex]P(\text{diamond) = }\frac{3}{30}=\frac{1}{10}[/tex]Therefore, the probability of selecting a club or a diamond is
[tex]\begin{gathered} P(\text{heart or diamond) = }\frac{11}{30}+\frac{1}{10} \\ P(\text{heart or diamond) = }\frac{7}{15} \end{gathered}[/tex]PART D: Theoretical probability of selecting a club or a diamond
We will find the probability of getting a club and then a diamond.
[tex]P(\text{club) = }\frac{13}{52}=\frac{1}{4}[/tex][tex]P(\text{diamond) = }\frac{13}{52}=\frac{1}{4}[/tex]Therefore, the probability of selecting a club or a diamond is
[tex]\begin{gathered} P(\text{heart or diamond) = }\frac{1}{4}+\frac{1}{4} \\ P(\text{heart or diamond) = }\frac{1}{2} \end{gathered}[/tex]
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