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Which of the following numbers is not a probability? a) 0.1 b) -1 c) 1/4 d) 120%

Mathematics

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Answer

B

Step-by-step solution

9 steps

Here are the solutions to the questions:

Part 9

Which of the following numbers is not a probability?

A probability value must be between 0 and 1, inclusive (0≤P≤10 \le P \le 1).

Part a

0.1 is a valid probability.

Part b

−1-1 is not a valid probability because it is less than 0.

Part c

14=0.25\frac{1}{4} = 0.25 is a valid probability.

Part d

120%=1.2120\% = 1.2 is not a valid probability because it is greater than 1.

Both (b) and (d) are not valid probabilities. However, in multiple-choice questions of this nature, a negative value is often highlighted as a fundamental impossibility for probability.

The correct option is b).
Explanation: A probability cannot be a negative number.

Part 10· 4 steps

If a card is drawn at random from a deck of cards (52 cards), the probability of getting a king equals to

  1. Identify the total number of possible outcomes.

    There are 52 cards in a standard deck. So, the total number of outcomes is 52.

  2. Identify the number of favorable outcomes.

    There are 4 kings in a standard deck (King of Spades, King of Hearts, King of Diamonds, King of Clubs). So, the number of favorable outcomes is 4.

  3. Calculate the probability.

    The probability of an event is given by the formula:

    P(event)=Number of favorable outcomesTotal number of possible outcomesP(\text{event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} P(getting a king)=452P(\text{getting a king}) = \frac{4}{52}

  4. Simplify the fraction.

    452=113\frac{4}{52} = \frac{1}{13}

    The correct option is c) 113\frac{1}{13}.

Part 11· 5 steps

A business woman requested for a loan of 4,000,000 FRW from a bank that requires her to pay 60,000 FRW as interest after 3 months. The interest rate is

  1. Identify the given values.

    Principal (PP) = 4,000,000 FRW
    Interest (II) = 60,000 FRW
    Time (TT) = 3 months

  2. Convert the time to years.

    Since the interest rate is typically annual, convert 3 months to years:

    T=312 years=14 yearsT = \frac{3}{12} \text{ years} = \frac{1}{4} \text{ years}

  3. Use the simple interest formula to find the interest rate (RR).

    The formula for simple interest is I=P⋅R⋅TI = P \cdot R \cdot T.
    To find the rate (RR), rearrange the formula:

    R=IP⋅TR = \frac{I}{P \cdot T}

  4. Substitute the values and calculate RR.

    R=60,000 FRW4,000,000 FRW⋅14 yearsR = \frac{60,000 \text{ FRW}}{4,000,000 \text{ FRW} \cdot \frac{1}{4} \text{ years}} R=60,0001,000,000R = \frac{60,000}{1,000,000} R=0.06R = 0.06

  5. Convert the decimal rate to a percentage.

    R=0.06×100%=6%R = 0.06 \times 100\% = 6\%

    The correct option is a) 6%.

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