Your brother is saving labels from soup cans. He removes the labels from three cans of pea soup,
five cans of vegetable soup and four cans of onion soup, and does not indicate the contents of the
twelve cans after removing the labels. You need two cans of onion soup to make your special
stew. What is the probability that two cans selected at random will both contain onion soup?
Thanks
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
4/12 * (4-1)/(12-1) = ?
To find the probability that two randomly selected cans will both contain onion soup, we need to calculate the probability of selecting two onion soup cans out of the total number of cans available.
First, let's determine the total number of cans available. Your brother removed the labels from 3 cans of pea soup, 5 cans of vegetable soup, and 4 cans of onion soup. So, the total number of cans is 3 + 5 + 4 = 12.
Next, let's calculate the number of ways to select two onion soup cans out of the available cans. Since there are 4 onion soup cans, we can choose two of them in 4C2 ways, which is calculated as:
4C2 = (4!)/(2!(4-2)!) = (4!)/(2!2!) = (4*3)/(2*1) = 6
Now, we need to calculate the total number of ways to select any two cans out of the available 12 cans. This can be calculated as 12C2, which is given by:
12C2 = (12!)/(2!(12-2)!) = (12!)/(2!10!) = (12*11)/(2*1) = 66
Finally, we can calculate the probability by dividing the number of ways to select two onion soup cans by the total number of ways to select any two cans:
Probability = Number of ways to select two onion soup cans / Total number of ways to select any two cans
Probability = 6/66 = 1/11
Therefore, the probability that two randomly selected cans will both contain onion soup is 1/11.