A fair spinner is divided into 8 congruent sectors numbered 1 through 8. A player spins th… — ACT

A fair spinner is divided into $8$ congruent sectors numbered $1$ through $8$ . A player spins the spinner twice in succession. How many of the $64$ possible outcomes result in a sum of the two spins that is strictly greater than $12$ ?

Cevap: 10 outcomes

Cevap

There are 10 outcomes that yield a sum strictly greater than 12.

Systematically listing all ordered pairs

(x, y)

from

\{1, 2, \dots, 8\} \times \{1, 2, \dots, 8\}

such that

x + y > 12

yields 4 outcomes for sum 13, 3 outcomes for sum 14, 2 outcomes for sum 15, and 1 outcome for sum 16, totaling 10 valid outcomes.

Adım Adım Çözüm

Determine the acceptable sums for the two spins

The possible sums strictly greater than 12 are 13, 14, 15, and 16.

Since each spin has a maximum value of 8, the maximum possible sum is 8 + 8 = 16.

Count the ordered pairs (spin 1, spin 2) for each valid sum

4 outcomes for sum 13, 3 outcomes for sum 14, 2 outcomes for sum 15, and 1 outcome for sum 16.

First and second spins are ordered, so (5,8) and (8,5) represent distinct outcomes.

Sum the outcome counts across all valid cases

4 + 3 + 2 + 1 = 10 outcomes.

The sets of outcomes for distinct sums are mutually exclusive.

Anahtar Kavram

Basic Probability and Counting Sample Space Outcomes

Tahmini Süre:1m 15s

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