Welcome to Westonci.ca, where you can find answers to all your questions from a community of experienced professionals. Join our platform to connect with experts ready to provide accurate answers to your questions in various fields. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.
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]
Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.
