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

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Trúc Chi 1 week 2021-09-04T17:44:36+00:00 1 Answers 0 views 0

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    2021-09-04T17:46:29+00:00

    Answer:

    (a) \frac{1}{7}

    (b) \frac{4}{7}

    (c) \frac{5}{7}

    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) = \frac{1}{7}

    (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) = \frac{1}{7}

    P(A) = \frac{1}{7}

    P(D) = \frac{1}{7}

    P(E) = \frac{1}{7}

    ∴ P(N) = \frac{1}{7} + \frac{1}{7} + \frac{1}{7} + \frac{1}{7}

    ∴ P(N) = \frac{4}{7}

    (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) = \frac{1}{7}

    P(B) = \frac{1}{7}

    P(C) = \frac{1}{7}

    P(D) = \frac{1}{7}

    P(E) = \frac{1}{7}

    P(H) = \frac{1}{7}

    ∴ P(S) = \frac{1}{7} + \frac{1}{7} + \frac{1}{7} + \frac{1}{7} + \frac{1}{7}

    ∴ P(S) = \frac{5}{7}

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