Students were surveyed to find out their favorite ice cream flavors. The results showed that 48% chose vanilla and 20% chose strawberry. In addition, 30% chose vanilla and strawberry What is the probability that a randomly selected student chose strawberry given that the student chose vanilla?
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To find the probability that a randomly selected student chose strawberry given that they chose vanilla, we need to use conditional probability.
Conditional probability looks at the probability of an event happening given that another event has already occurred. In this case, we want to find the probability of choosing strawberry given that the student chose vanilla.
Let's start by calculating the probability of choosing vanilla and strawberry. The question states that 30% of the students chose both flavors. This means that out of 100 students, 30 chose both strawberries and vanillas.
Next, we need to find the probability of choosing vanilla. The question states that 48% of the students chose vanilla. So, out of 100 students, 48 chose vanilla.
To calculate the probability of choosing strawberry given that the student chose vanilla, we need to divide the probability of choosing both flavors by the probability of choosing vanilla.
Probability(strawberry given vanilla) = Probability(strawberry and vanilla) / Probability(vanilla)
Probability(strawberry given vanilla) = 30 / 48
Simplifying this fraction, we get:
Probability(strawberry given vanilla) ≈ 0.625 or 62.5%
Therefore, the probability that a randomly selected student chose strawberry given that they chose vanilla is approximately 0.625 or 62.5%.
To find the probability that a student chose strawberry given that they chose vanilla, we need to use conditional probability.
The formula for conditional probability is:
P(A|B) = P(A and B) / P(B)
In this case, A represents choosing strawberry and B represents choosing vanilla.
To start, we need to find P(A and B), which is the probability of choosing both strawberry and vanilla. From the given information, we know that 30% of students chose both flavors. So, P(A and B) = 0.30.
Next, we need to find P(B), which is the probability of choosing vanilla. From the given information, we know that 48% of students chose vanilla, so P(B) = 0.48.
Finally, we can plug these values into the formula:
P(A|B) = P(A and B) / P(B)
= 0.30 / 0.48
≈ 0.625
Therefore, the probability that a randomly selected student chose strawberry given that they chose vanilla is approximately 0.625 or 62.5%.