there are 12 sweets in a bag. 7 of the sweets are strawberry flavou. 5 of the sweets are lime flavour. harriet takes 2 sweets at random work out the probability that she takes at least one strawberry sweet.
you go this from the unit test 10
To find the probability that Harriet takes at least one strawberry sweet, we need to calculate the probability of the complement event, which is the probability of not taking any strawberry sweet.
First, let's calculate the total number of possible outcomes. Harriet is taking two sweets at random from a bag of 12. The total number of ways to select 2 sweets from 12 is given by the combination formula, denoted as C(n, r), which calculates the number of ways to choose r objects from a set of n distinct objects. In this case, n = 12 and r = 2. Therefore, the total number of possible outcomes is:
C(12, 2) = 12! / (2!(12-2)!) = 66
Next, let's calculate the number of ways to select 2 sweets that are not strawberry flavor. There are 5 lime flavor sweets in the bag, so the number of ways to choose 2 lime sweets is:
C(5, 2) = 5! / (2!(5-2)!) = 10
Since Harriet wants to take at least one strawberry sweet, we subtract the number of ways to not take any strawberry sweet from the total number of outcomes. Therefore, the number of outcomes where Harriet takes at least one strawberry sweet is:
Number of outcomes with at least one strawberry sweet = Total number of outcomes - Number of outcomes with no strawberry sweet
= 66 - 10
= 56
Finally, we can calculate the probability by dividing the number of favorable outcomes (taking at least one strawberry sweet) by the total number of possible outcomes.
Probability of taking at least one strawberry sweet = Number of outcomes with at least one strawberry sweet / Total number of possible outcomes
= 56 / 66
≈ 0.8485
Therefore, the probability that Harriet takes at least one strawberry sweet is approximately 0.848 or 84.8%.
at least one? Pr(at least one)=1-prob(none)
1-5/12*4/11