Respuesta :
In this question, we need to find the probability of pulling a red or brown candy from a bag.
We know that the bag contains the next amount of candies:
• 5 yellow candies
,• 11 red candies
,• 4 green candies
,• 12 blue candies
,• 7 brown candies
Therefore, in total, we have 39 candies.
Then the probability of pulling a red candy is:
[tex]P(\text{red)}=\frac{11}{39}[/tex]The probability of pulling a brown candy is:
[tex]P(\text{brown)}=\frac{7}{39}[/tex]Now, we know that the general formula for the probability of two events is given by:
[tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)[/tex]However, in this case, we do not have any probability that both events happen at the same time - in other words, they are mutually exclusive events. Therefore, we have:
[tex]\begin{gathered} P(R\cup B)=P(R)+P(B)-P(R\cap B) \\ P(R\cup B)=\frac{11}{39}+\frac{7}{39}=\frac{18}{39} \\ P(R\cup B)=\frac{18}{39} \end{gathered}[/tex]Therefore, in summary, the probability that a red or brown candy is pulled from the bag is 18/39 (option A.)
