To find the probability that the ticket is worth at least [tex]$75, we need to consider the probabilities of winning both $[/tex]75 and [tex]$100 prizes. Hence, we will sum these probabilities.
1. Probability of winning $[/tex]75: According to the given information, the probability of winning a [tex]$75 prize is 0.004.
2. Probability of winning $[/tex]100: According to the given information, the probability of winning a [tex]$100 prize is 0.003.
3. Probability of ticket being worth at least $[/tex]75:
To find this, we add the probabilities of winning the [tex]$75 and $[/tex]100 prizes.
[tex]\[ \text{Probability of at least $75 prize} = \text{Probability of $75 prize} + \text{Probability of $100 prize} \][/tex]
[tex]\[ \text{Probability of at least $75 prize} = 0.004 + 0.003 \][/tex]
When we sum these probabilities, we get:
[tex]\[ \text{Probability of at least $75 prize} = 0.004 + 0.003 = 0.007 \][/tex]
Therefore, the probability that the ticket is worth at least $75 is [tex]\(0.007\)[/tex].
