Share
Jade has seven cards. Each card is labeled with a letter. A B C D E F G H J Jade picks one of her cards at random. Find the probability that
Question
Jade has seven cards. Each card is labeled with a letter. A B C D E F G H J Jade picks one of her cards at random. Find the probability that the card she picks is a) labelled F, b) labelled with a letter in her name JADE c) labelled with a letter that has at least one line of symmetry
in progress
0
Mathematics
3 years
2021-09-04T17:44:36+00:00
2021-09-04T17:44:36+00:00 1 Answers
35 views
0
Answers ( )
Answer:
(a)![Rendered by QuickLaTeX.com \frac{1}{7}](https://documen.tv/wp-content/ql-cache/quicklatex.com-ad9e98aa7250277761bf01899f916f02_l3.png)
(b)![Rendered by QuickLaTeX.com \frac{4}{7}](https://documen.tv/wp-content/ql-cache/quicklatex.com-35845ae536fceba6c022b44a65c61d9f_l3.png)
(c)![Rendered by QuickLaTeX.com \frac{5}{7}](https://documen.tv/wp-content/ql-cache/quicklatex.com-ca0b99a2ec22006d674eb42e47fe6367_l3.png)
Step-by-step explanation:
Probability (P) of an event is the likelihood that the event will occur. It is given by;
P = number of favourable outcomes ÷ total number of events in the sample space.
Given letters of cards:
A B C D E F G H J
∴ Total number of events in sample space is actually the number of cards which is 7
If a card is picked at random;
(a) the probability P(F), that it is labelled F is given by;
P(F) = number of favourable outcomes ÷ total number of events in the sample space.
The number of favourable outcomes for picking an F = 1 since there is only one card labelled with F.
∴ P(F) = 1 ÷ 7
=> P(F) =![Rendered by QuickLaTeX.com \frac{1}{7}](https://documen.tv/wp-content/ql-cache/quicklatex.com-ad9e98aa7250277761bf01899f916f02_l3.png)
(b) the probability P(N), that it is labelled with a letter in her name JADE is given by;
P(N) = P(J) + P(A) + P(D) + P(E)
Where;
P(J) = Probability that it is labelled J
P(A) = Probability that it is labelled A
P(D) = Probability that it is labelled D
P(E) = Probability that it is labelled E
P(J) =
P(A) =
P(D) =
P(E) =
∴ P(N) =
+
+
+
∴ P(N) =![Rendered by QuickLaTeX.com \frac{4}{7}](https://documen.tv/wp-content/ql-cache/quicklatex.com-35845ae536fceba6c022b44a65c61d9f_l3.png)
(c) the probability P(S), that it is labelled with a letter that has at least one line of symmetry is;
P(S) = P(A) + P(B) + P(C) + P(D) + P(E) + P(H)
Where;
P(A) = Probability that it is labelled A
P(B) = Probability that it is labelled B
P(C) = Probability that it is labelled C
P(D) = Probability that it is labelled D
P(E) = Probability that it is labelled E
P(H) = Probability that it is labelled H
Cards with letters A, B, C, D, E and H are selected because these letters have at least one line of symmetry. A line of symmetry is a line that cuts an object into two identical halves. Letters A, B, C, D, E and H can each be cut into two identical halves.
P(A) =![Rendered by QuickLaTeX.com \frac{1}{7}](https://documen.tv/wp-content/ql-cache/quicklatex.com-ad9e98aa7250277761bf01899f916f02_l3.png)
P(B) =![Rendered by QuickLaTeX.com \frac{1}{7}](https://documen.tv/wp-content/ql-cache/quicklatex.com-ad9e98aa7250277761bf01899f916f02_l3.png)
P(C) =![Rendered by QuickLaTeX.com \frac{1}{7}](https://documen.tv/wp-content/ql-cache/quicklatex.com-ad9e98aa7250277761bf01899f916f02_l3.png)
P(D) =![Rendered by QuickLaTeX.com \frac{1}{7}](https://documen.tv/wp-content/ql-cache/quicklatex.com-ad9e98aa7250277761bf01899f916f02_l3.png)
P(E) =![Rendered by QuickLaTeX.com \frac{1}{7}](https://documen.tv/wp-content/ql-cache/quicklatex.com-ad9e98aa7250277761bf01899f916f02_l3.png)
P(H) =![Rendered by QuickLaTeX.com \frac{1}{7}](https://documen.tv/wp-content/ql-cache/quicklatex.com-ad9e98aa7250277761bf01899f916f02_l3.png)
∴ P(S) =
+
+
+
+ ![Rendered by QuickLaTeX.com \frac{1}{7}](https://documen.tv/wp-content/ql-cache/quicklatex.com-ad9e98aa7250277761bf01899f916f02_l3.png)
∴ P(S) =![Rendered by QuickLaTeX.com \frac{5}{7}](https://documen.tv/wp-content/ql-cache/quicklatex.com-ca0b99a2ec22006d674eb42e47fe6367_l3.png)