Question

following a flood 120 tins were removed from dan’s corner shop. unfortunately, the water washed off all the labels of the tins. 50 contained pet food, 20 contained peas, 35 contained beans, and the rest contained soup. dan randomly selects a tin. find the probability that it: a) contains soup b) does not contain pet food 2) dan randomly selects two tins without replacement. find the probability that: both contain peas, one pet food, and the other contains peas. 3) dan randomly selects 10 cans. find the probability that at least one contains beans.

Answer 1

The probability of a tin containing soup is 0.125, and the probability of a tin not containing pet food is approximately 0.583. To find these probabilities, we subtract the quantities of known tins from the total and use ratios.

Step-by-step explanation:

Given 120 tins with 50 containing pet food, 20 peas, 35 beans, and the rest soup, we can find the probability of a randomly selected tin containing soup by subtracting the known quantities from the total. To determine the probability of a tin not containing pet food, we calculate the ratio of non-pet food tins to total tins.

For the second part, when selecting two tins without replacement, we use the hypergeometric distribution to find the probability that both contain peas and the probability that one contains pet food and the other peas.

For the third part, selecting 10 cans and finding the probability that at least one contains beans also uses the hypergeometric distribution.
Probability of a tin containing soup: The rest are soup tins, so there are 120 - (50 + 20 + 35) = 15 soup tins. The probability is 15/120 = 1/8 or 0.125.

Probability of a tin not containing pet food: There are 120 - 50 = 70 tins that do not contain pet food. The probability is 70/120 = 7/12 or approximately 0.583.