Question

1. this venn diagram shows the results of a survey identifying what colors some children liked.

9a what is the probability of a child liking blue and yellow?
probability = \\(\frac{5}{19}\\)
9b what is the probability of a child liking blue or yellow but not both?
probability = enter your next step here

Explanation:

Step1: Recall total number of children

From part 9a, we know the probability of liking both is $\frac{5}{19}$, so total number of children $n = 19$ (since probability is favorable over total, so total is 19 as numerator for both is 5). Also, there are 3 children who like neither (from Venn diagram's outside region).

Step2: Find number of children who like only blue or only yellow

Let's assume the number of children who like only blue is $A$, only yellow is $B$, both is $5$, and neither is $3$. So total $A + B + 5 + 3 = 19$. Then $A + B = 19 - 5 - 3 = 11$. The number of children who like blue or yellow but not both is $A + B$, which is 11.

Step3: Calculate the probability

Probability is $\frac{\text{Number of children who like only blue or only yellow}}{\text{Total number of children}}=\frac{11}{19}$.

Answer:

$\frac{11}{19}$