Respuesta :
The probability that you choose a bottle of apple juice followed by a bottle of grape juice is (24 / 91)
What is probability?
Probability = (Number of desired outcomes) / (Total number of outcomes)
What are dependent events?
Dependent events in probability are events whose occurrence of one affects the probability of occurrence of the other.
What is the multiplication rule?
We can use the multiplication rule to find the probability of dependent events.
P(A∩B) = P(A) × P(B|A), where P(B|A) is the conditional probability of event B, given that event A has already occurred.
In probability theory, conditional probability is a measure of the probability of an event occurring, given that another event has already occurred.
In the given question what we have is as follows:
- A basket of 6 bottles of apple juice,
- 8 bottles of grape juice.
Now, we choose a bottle without looking and then choose another bottle. Here there are two dependent events.
According to the question, the probability of choosing a bottle of apple juice first is,
= (Total number of bottles of apple juice) / (Total number of bottles in the basket)
= 6/(6+8)
= 6/14
Then, to find the probability of choosing a bottle of apple juice followed by a bottle of grape juice we will apply the multiplication rule,
First, we will find the conditional probability that is,
P(choosing a bottle of grape juice | choosing a bottle of apple juice)
= (Total number of bottles of grape juice) / ( total number of bottles)
= 8/(5+8), because we already picked a bottle of apple juice
= 8/13
Finally, we will apply the multiplication rule,
P(choosing a bottle of apple juice ∩ choosing a bottle of grape juice)
= P(choosing a bottle of apple juice) × P(choosing a bottle of grape juice | choosing a bottle of apple juice)
= (6/14) × (8/13)
By rearranging we get,
= (6 × 8) / (14 × 13)
By simplifying we get,
= 48 / 182
By further simplifying we get,
= 24 / 91
Therefore, the probability of choosing a bottle of apple juice followed by a bottle of grape juice is (24 / 91)
Know more about how to solve probability related questions click here - brainly.com/question/15207891
#SPJ2
