Gabriel has these cans of soup in his kitchen cabinet 2 cans of tomato soup,3 cans of chicken soup,2 cans of cheese soup,2 can of potato soup,1 can of beef soup. Gabriel will randomly choose a can of soup.Then he will put it back and randomly choose another can of soup.what is the probability that he will choose a can of tomato soup and then a can of cheese soup?
To find the probability of Gabriel first choosing a can of tomato soup and then a can of cheese soup, we need to consider the total number of possible outcomes and the number of desired outcomes.
Total number of outcomes = Total number of cans of soup = 2 + 3 + 2 + 2 + 1 = 10
Number of desired outcomes = Number of cans of tomato soup * Number of cans of cheese soup = 2 * 2 = 4
Therefore, the probability of Gabriel choosing a can of tomato soup and then a can of cheese soup is:
P = Number of desired outcomes / Total number of outcomes
P = 4 / 10
P = 2 / 5
P = 0.4 or 40%
To find the probability that Gabriel will choose a can of tomato soup and then a can of cheese soup, we need to calculate the probability of each event happening and then multiply them together.
Step 1: Calculate the probability of choosing a can of tomato soup.
There are a total of 10 cans of soup in Gabriel's cabinet, and 2 of them are tomato soup. Therefore, the probability of choosing a can of tomato soup on the first try is 2/10 or 1/5.
Step 2: Calculate the probability of choosing a can of cheese soup after choosing a can of tomato soup.
Since Gabriel puts the can back after the first selection, the total number of cans of soup remains the same for the second selection. So, there are still 10 cans of soup. However, now there is only 1 can of tomato soup left, and 2 cans of cheese soup. Therefore, the probability of choosing a can of cheese soup after choosing a can of tomato soup is 2/10 or 1/5.
Step 3: Multiply the probabilities.
To find the overall probability of both events happening, we multiply the individual probabilities:
(1/5) * (1/5) = 1/25 or 0.04.
Therefore, the probability that Gabriel will choose a can of tomato soup and then a can of cheese soup is 1/25 or 0.04.