To determine the probability of picking a gray or white pebble from the bag, let's follow these steps:
1. Count the total number of pebbles in the bag:
- Number of brown pebbles = 11
- Number of black pebbles = 16
- Number of gray pebbles = 19
- Number of white pebbles = 9
The total number of pebbles is given by the sum of all these quantities:
[tex]\[
\text{Total pebbles} = 11 + 16 + 19 + 9 = 55
\][/tex]
2. Determine the number of favorable outcomes:
- Favorable outcomes are the pebbles that are either gray or white.
- Number of gray pebbles = 19
- Number of white pebbles = 9
The total number of favorable outcomes (gray or white pebbles) is:
[tex]\[
\text{Favorable outcomes} = 19 + 9 = 28
\][/tex]
3. Calculate the probability:
The probability [tex]\( P(\text{gray or white}) \)[/tex] is the ratio of the number of favorable outcomes to the total number of pebbles:
[tex]\[
P(\text{gray or white}) = \frac{\text{Favorable outcomes}}{\text{Total pebbles}} = \frac{28}{55}
\][/tex]
Simplifying the fraction may not be necessary here, so we can leave the answer in this form or convert it to a decimal fraction. After converting it to a decimal, we get:
[tex]\[
P(\text{gray or white}) = \frac{28}{55} \approx 0.5091
\][/tex]
Thus, the probability that a randomly picked pebble is either gray or white is:
[tex]\[
P(\text{gray or white}) = \boxed{0.5091}
\][/tex]
