Question

Consider 10 balls each having different colors including a blue ball. If 6 balls are selected randomly, the probability of the blue ball being selected is

• A. 0.3
• B. 0.4
• C. 0.6
• D. 0.8

Hint:

In problems involving probability of selecting a specific item (like a blue ball), use combinations to determine the number of ways to select the items.

Answer 1

The Correct Option is C

Step 1: Total number of balls.
There are 10 balls in total, one of which is blue.
Step 2: Number of balls selected.
We are selecting 6 balls out of 10 randomly.
Step 3: Probability calculation.
The probability of selecting the blue ball can be found using the formula: \[ P(\text{Blue ball selected}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} \] The number of favorable outcomes is the number of ways to select 5 balls from the remaining 9 balls, which is \( \binom{9}{5} \).
The total number of possible outcomes is the number of ways to select 6 balls from 10, which is \( \binom{10}{6} \).
Thus, the probability is: \[ P = \frac{\binom{9}{5}}{\binom{10}{6}} = \frac{126}{210} = 0.6 \] Final Answer: \[ \boxed{0.6} \]