11. A basket contains the following pieces of fruit: three apples to oranges two pairs two bananas and five peaches. Jack pics of fruit at random and does not replace it then, Bethany pics of fruit at random. what is the probability that Jack gets a peach and Bethany gets an orange?
10/27
5/91
5/98
93/182
Thnx for the help!
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
5/14 * 2/(14-1) = ?
To find the probability that Jack gets a peach and Bethany gets an orange, we need to consider the total number of possible outcomes as well as the number of favorable outcomes.
First, let's calculate the total number of possible outcomes. Since Jack picks a fruit at random and does not replace it, the number of possible outcomes will decrease with each pick. We start with 3 apples, 2 oranges, 2 pairs, 2 bananas, and 5 peaches, giving us a total of 14 fruits.
For the first pick, Jack has 14 options. After Jack picks a fruit, there will be 13 fruits left for Bethany's pick. The probability that Jack picks a peach is 5/14, as there are 5 peaches out of the total of 14 fruits.
Now, let's consider the number of favorable outcomes, where Jack gets a peach and Bethany gets an orange. Since Jack already picked one fruit, there are now 4 peaches and 2 oranges left. Therefore, the probability that Bethany picks an orange is 2/13.
To calculate the joint probability (probability of both events happening), we multiply the probability of Jack picking a peach (5/14) by the probability of Bethany picking an orange (2/13):
(5/14) * (2/13) = 10/182 = 5/91
Therefore, the probability that Jack gets a peach and Bethany gets an orange is 5/91.