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A bag contains 11 brown, 16 black, 19 gray, and 9 white pebbles. You pick one pebble at random. Find the probability that it is gray or white.

[tex]\[ P(\text{gray or white}) = \][/tex]
[tex]\[\square\][/tex]
[tex]\[\square\][/tex]

Sagot :

GinnyAnsweridn
To solve the problem of finding the probability that a randomly picked pebble is either gray or white, follow these steps:

1. Determine the total number of pebbles in the bag by adding up the number of pebbles of each color:
[tex]\[ \text{Total pebbles} = 11 \text{ (brown)} + 16 \text{ (black)} + 19 \text{ (gray)} + 9 \text{ (white)} \][/tex]
[tex]\[ \text{Total pebbles} = 55 \][/tex]

2. Calculate the total number of pebbles that are either gray or white by summing up the number of gray pebbles and white pebbles:
[tex]\[ \text{Gray or white pebbles} = 19 \text{ (gray)} + 9 \text{ (white)} \][/tex]
[tex]\[ \text{Gray or white pebbles} = 28 \][/tex]

3. Calculate the probability of picking a gray or white pebble. The probability is defined as the ratio of the number of favorable outcomes (gray or white pebbles) to the total number of possible outcomes (total pebbles):
[tex]\[ P(\text{gray or white}) = \frac {\text{Number of gray or white pebbles}}{\text{Total number of pebbles}} \][/tex]
[tex]\[ P(\text{gray or white}) = \frac{28}{55} \][/tex]

4. Simplify the fraction if possible. In this case, the fraction [tex]\(\frac{28}{55}\)[/tex] cannot be simplified further.

Thus, the probability of picking a gray or white pebble is:
[tex]\[ P(\text{gray or white}) \approx 0.509 \][/tex]
Heatheridn

Answer:

[tex]\dfrac{28}{50}, 0.509090909, \text{ or about }50.91\%[/tex]

Step-by-step explanation:

   To find the probability that a pebble picked at random is gray or white, we will divide the number of gray or white marbles by the total number of marbles.

       [tex]\displaystyle \frac{\text{Number of specific outcomes}}{\text{Number of total outcomes}}=\frac{\text{Gray or white}}{\text{Pebbels in bag}} =\frac{19+9}{11+16+19+9} =\frac{28}{55}[/tex]

   We can compute this fraction to find a decimal value. Then, we can multiply it by 100 to find a percentage.

       [tex]\displaystyle \frac{28}{55} =0.509090909\;\;\;\;\;0.509090909*100\approx50.91\%[/tex]

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