To determine the number of customers who ate curry, we first need to find the probability of a customer eating curry. We are given the probabilities for the other meal options:
- Probability of eating Chilli: [tex]\(0.15\)[/tex]
- Probability of eating Stew: [tex]\(0.3\)[/tex]
- Probability of eating Pizza: [tex]\(0.1\)[/tex] (since [tex]\(\frac{1}{10} = 0.1\)[/tex])
Since the total probability for all meals must sum up to 1, we can calculate the probability of eating curry by subtracting the probabilities of the other meals from 1:
[tex]\[
\text{Probability of eating Curry} = 1 - (\text{Probability of eating Chilli} + \text{Probability of eating Stew} + \text{Probability of eating Pizza})
\][/tex]
Substitute the given probabilities:
[tex]\[
\text{Probability of eating Curry} = 1 - (0.15 + 0.3 + 0.1)
\][/tex]
[tex]\[
\text{Probability of eating Curry} = 1 - 0.55 = 0.45
\][/tex]
Now, knowing that Sumaya asked 300 customers, we need to find how many of these customers we would expect to have eaten curry. We do this by multiplying the total number of customers by the probability of eating curry:
[tex]\[
\text{Expected number of customers who ate Curry} = \text{Total customers} \times \text{Probability of eating Curry}
\][/tex]
Substitute the values:
[tex]\[
\text{Expected number of customers who ate Curry} = 300 \times 0.45 = 135
\][/tex]
So, based on the probabilities given and the calculations, we would expect 135 out of the 300 customers to have eaten curry.
