Silvia has a collection of stamps from around the world as listed below.
4 stamps from Mexico
3 stamps from Peru
6 stamps from Germany
2 stamps from Tonga
5 stamps from New Zealand
She places them all in a box and randomly draws one.
What is the probability that Silvia draws a stamp from New Zealand?
What is the probability that Silvia draws a stamp from either Germany or Tonga?
What is the probability that Silvia draws a stamp from either Peru or Mexico?
What is the probability that Silvia does not draw a stamp from Tonga?
and explain
Answers:
1. The probability that Silvia draws a stamp from New Zealand is 5/20 or 1/4. This is because there are 5 stamps from New Zealand out of a total of 20 stamps in the collection.
2. The probability that Silvia draws a stamp from either Germany or Tonga is 8/20 or 2/5. This is because there are 6 stamps from Germany and 2 stamps from Tonga, for a total of 8 stamps out of 20.
3. The probability that Silvia draws a stamp from either Peru or Mexico is 7/20 or 0.35. This is because there are 4 stamps from Mexico and 3 stamps from Peru, for a total of 7 stamps out of 20.
4. The probability that Silvia does not draw a stamp from Tonga is 18/20 or 9/10. This is because there are 20 stamps in total, and 2 of them are from Tonga, so there are 18 stamps that are not from Tonga. Therefore, the probability of not drawing a stamp from Tonga is 18/20 or 9/10.
To find the probability, we need to divide the number of desired outcomes by the total number of possible outcomes.
1. Probability of drawing a stamp from New Zealand:
There are a total of 4 + 3 + 6 + 2 + 5 = 20 stamps in the box. Out of these, 5 stamps are from New Zealand. So the probability of drawing a stamp from New Zealand is:
P(New Zealand) = 5/20 = 1/4 = 0.25 (or 25%).
2. Probability of drawing a stamp from either Germany or Tonga:
The total number of stamps from Germany and Tonga combined is 6 + 2 = 8. So the probability of drawing a stamp from either Germany or Tonga is:
P(Germany or Tonga) = 8/20 = 2/5 = 0.4 (or 40%).
3. Probability of drawing a stamp from either Peru or Mexico:
The total number of stamps from Peru and Mexico combined is 3 + 4 = 7. So the probability of drawing a stamp from either Peru or Mexico is:
P(Peru or Mexico) = 7/20 = 0.35 (or 35%).
4. Probability of not drawing a stamp from Tonga:
Since there are 2 stamps from Tonga, the probability of not drawing a stamp from Tonga is the complement of drawing a stamp from Tonga. So the probability is:
P(not Tonga) = 1 - P(Tonga) = 1 - (2/20) = 1 - 1/10 = 9/10 = 0.9 (or 90%).
In summary:
1. Probability of drawing a stamp from New Zealand = 1/4 = 0.25 (or 25%).
2. Probability of drawing a stamp from either Germany or Tonga = 2/5 = 0.4 (or 40%).
3. Probability of drawing a stamp from either Peru or Mexico = 7/20 = 0.35 (or 35%).
4. Probability of not drawing a stamp from Tonga = 9/10 = 0.9 (or 90%).