A container contains 4 ruby beads, 5 sapphire beads, and 6 emerald beads. If one bead is selected at random, what is the probability that it is not a sapphire bead?

The correct option is $\frac{10}{15}$.

Step 1: Determine the total number of beads in the container.
The container contains:
• Ruby beads = 4
• Sapphire beads = 5
• Emerald beads = 6

Total number of beads = 4 + 5 + 6 = 15

Step 2: Find the number of favorable outcomes.
We want to find the probability of selecting a bead that is not a sapphire bead. The beads that are not sapphire are the ruby beads and the emerald beads.

Number of beads that are not sapphire = Ruby beads + Emerald beads = 4 + 6 = 10

Step 3: Calculate the probability.
The probability of an event is given by the ratio of the number of favorable outcomes to the total number of possible outcomes:

$\text{Probability}=\frac{\text{Number of non-sapphire beads}}{\text{Total number of beads}}$

$\text{Probability}=\frac{10}{15}$

Thus, the probability that the randomly selected bead is not a sapphire bead is $\frac{10}{15}$.