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Zorluk: KolayBasic Probability and Counting Methods

A fair game spinner is divided into 88 equal sectors numbered 11 through 88. If Maya spins the spinner once, what is the probability that the spinner lands on a number strictly greater than 55?

  1. 38\frac{3}{8}Cevap
  2. B
    58\frac{5}{8}
  3. C
    35\frac{3}{5}
  4. D
    14\frac{1}{4}
  5. E
    12\frac{1}{2}

Cevap

The probability that the spinner lands on a number strictly greater than 5 is 38\frac{3}{8}.
The sample space consists of 8 equally likely outcomes: {1, 2, 3, 4, 5, 6, 7, 8}. The event 'landing on a number strictly greater than 5' consists of 3 outcomes: {6, 7, 8}. The probability is the ratio of favorable outcomes to total outcomes, which gives 3/8.

Adım Adım Çözüm

1
Determine the total number of possible outcomes in the sample space.
The total number of equal sectors is 88, so total outcomes = 88.
The spinner is divided into 8 equal sections numbered 1 through 8.
2
Identify the favorable outcomes that satisfy the condition 'strictly greater than 5'.
The numbers strictly greater than 55 are 66, 77, and 88. Thus, there are 33 favorable outcomes.
Strictly greater than 5 excludes 5 itself.
3
Calculate the probability using the basic probability formula.
P(greater than 5)=Number of favorable outcomesTotal number of outcomes=38P(\text{greater than } 5) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{3}{8}.
Theoretical probability is the ratio of favorable outcomes to total sample space outcomes.

Anahtar Kavram

Basic Probability of Simple Events
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Basic Probability and Counting Methods

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