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A bag contains five white beads, three black beads and two yellow beads. If a bead is picked from the bag at random, find the probability of picking a yellow bead and the probability of picking a bead which is not yellow. Express each probability as a decimal and as a percentage.

Mathematics

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:
A spinner wheel has four equal sectors: red, blue, yellow, and green. It is spun once.

a) Find the probability of the pointer resting on red.

  1. Identify the total number of possible outcomes.

    There are 4 equal sectors: red, blue, yellow, green. So, the total number of outcomes is 4.

  2. Identify the number of favorable outcomes (resting on red).

    There is 1 red sector. So, the number of favorable outcomes is 1.

  3. Calculate the probability.

    P(red)=Number of red sectorsTotal number of sectorsP(\text{red}) = \frac{\text{Number of red sectors}}{\text{Total number of sectors}} P(red)=14P(\text{red}) = \frac{1}{4}

    The probability of the pointer resting on red is 14\boxed{\frac{1}{4}}.

    b) Express the probability as a decimal and as a percentage.

  4. Convert the probability to a decimal.

    14=0.25\frac{1}{4} = 0.25

  5. Convert the decimal to a percentage.

    0.25×100%=25%0.25 \times 100\% = 25\%

    The probability as a decimal is 0.25\boxed{0.25} and as a percentage is 25%\boxed{25\%}.

    :
    A bag contains five white beads, three black beads, and two yellow beads. A bead is picked from the bag at random.

  6. Calculate the total number of beads in the bag.

    Total beads = 5(white)+3(black)+2(yellow)=105 (\text{white}) + 3 (\text{black}) + 2 (\text{yellow}) = 10 beads.

    a) Find the probability of picking a yellow bead.

  7. Identify the number of yellow beads.

    There are 2 yellow beads.

  8. Calculate the probability of picking a yellow bead.

    P(yellow bead)=Number of yellow beadsTotal number of beadsP(\text{yellow bead}) = \frac{\text{Number of yellow beads}}{\text{Total number of beads}} P(yellow bead)=210P(\text{yellow bead}) = \frac{2}{10} P(yellow bead)=15P(\text{yellow bead}) = \frac{1}{5}

    The probability of picking a yellow bead is 15\boxed{\frac{1}{5}}.

    b) Find the probability of picking a bead which is not yellow.

  9. Identify the number of beads that are not yellow.

    Number of non-yellow beads = Number of white beads + Number of black beads
    Number of non-yellow beads = 5+3=85 + 3 = 8 beads.

  10. Calculate the probability of picking a non-yellow bead.

    P(not yellow bead)=Number of non-yellow beadsTotal number of beadsP(\text{not yellow bead}) = \frac{\text{Number of non-yellow beads}}{\text{Total number of beads}} P(not yellow bead)=810P(\text{not yellow bead}) = \frac{8}{10} P(not yellow bead)=45P(\text{not yellow bead}) = \frac{4}{5}

    The probability of picking a bead which is not yellow is 45\boxed{\frac{4}{5}}.

    c) Express each probability as a decimal and as a percentage.
    For picking a yellow bead:

  11. Convert the probability to a decimal.

    15=0.2\frac{1}{5} = 0.2

  12. Convert the decimal to a percentage.

    0.2×100%=20%0.2 \times 100\% = 20\%

    The probability of picking a yellow bead as a decimal is 0.2\boxed{0.2} and as a percentage is 20%\boxed{20\%}.

    For picking a bead which is not yellow:

  13. Convert the probability to a decimal.

    45=0.8\frac{4}{5} = 0.8

  14. Convert the decimal to a percentage.

    0.8×100%=80%0.8 \times 100\% = 80\%

    The probability of picking a non-yellow bead as a decimal is 0.8\boxed{0.8} and as a percentage is 80%\boxed{80\%}.

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