Math / Data & Statistics

QuestionA bag contains 5 blue, 4 green and 2 purple counters. One counter is picked at random. What is the probability that the counter is green or blue? Give your answer as a fraction.

Studdy Solution

STEP 1

1. The bag contains a total of 5 blue, 4 green, and 2 purple counters.
2. The probability of an event is calculated as the number of favorable outcomes divided by the total number of possible outcomes.
3. The events "picking a green counter" and "picking a blue counter" are mutually exclusive.

STEP 2

1. Calculate the total number of counters.
2. Calculate the number of favorable outcomes (green or blue counters).
3. Calculate the probability as a fraction.

STEP 3

Calculate the total number of counters in the bag:
$5 \text{ (blue)} + 4 \text{ (green)} + 2 \text{ (purple)} = 11 \text{ counters}$

STEP 4

Calculate the number of favorable outcomes (green or blue counters):
$5 \text{ (blue)} + 4 \text{ (green)} = 9 \text{ favorable outcomes}$

STEP 5

Calculate the probability of picking a green or blue counter:
$\frac{\text{Number of favorable outcomes}}{\text{Total number of counters}} = \frac{9}{11}$
The probability that the counter is green or blue is:
$\boxed{\frac{9}{11}}$

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