QuestionUse the tree diagram below to work out the probability that at least one of the two customers buys a vanilla ice cream. Give your answer as a fraction in its simplest form.
Studdy Solution
STEP 1
1. The tree diagram represents a sequence of independent events involving two customers.
2. Each customer independently chooses between vanilla and strawberry ice cream.
3. The probabilities for each choice remain constant for both customers.
STEP 2
1. Calculate the probability of both customers choosing strawberry.
2. Use complementary probability to find the probability of at least one customer choosing vanilla.
STEP 3
Calculate the probability that both customers choose strawberry.
- Probability that the first customer chooses strawberry: .
- Probability that the second customer chooses strawberry given the first chose strawberry: .
The combined probability for both choosing strawberry is:
STEP 4
Use complementary probability to find the probability that at least one customer chooses vanilla.
- The probability of at least one choosing vanilla is the complement of both choosing strawberry.
Simplify the fraction:
- The greatest common divisor of 24 and 49 is 1, so the fraction is already in its simplest form.
The probability that at least one customer buys a vanilla ice cream is:
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