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?
A. 10/27
B. 5/91
C. 5/98
D. 93/182
I don't really understand how to fully do this, if you could give me a formula or help me out, I'll be very thankful
A basket contains the following pieces of fruit: 3 apples, 2 oranges, 2 bananas, 2 pears, and 5 peaches. Jack picks a fruit at random and does not replace it. Then Bethany picks a fruit at random. What is the probability that Jack gets a peach and Bethany gets an orange?
I'm so sorry, I didn't pay much attention whilst writing, but this is coming straight from the work I was assigned
Jack ... 5 peaches in 14 pieces of fruit
... probability of peach is ... 5/14
Bethany ... 2 oranges in 13 pieces of fruit
... probability of orange is ... 2/13
the probability of both events happening is the product of the individual probabilities
To find the probability that Jack gets a peach and Bethany gets an orange, we need to consider the total number of possible outcomes and the number of favorable outcomes.
First, let's calculate the total number of possible outcomes.
The total number of fruits in the basket is:
3 (apples) + 2 (pairs) + 2 (bananas) + 5 (peaches) = 12
Since Jack picks fruit without replacement, there will be 11 fruits left in the basket when Bethany picks.
So, the total number of possible outcomes for both Jack and Bethany is given by:
12 * 11 = 132
Next, let's calculate the number of favorable outcomes, which is the number of ways for Jack to pick a peach and Bethany to pick an orange.
The number of peaches is 5, and after Jack picks one, there will be 4 peaches left in the basket. Similarly, the number of oranges is 2, and after Bethany picks one, there will be 1 orange left in the basket.
So, the number of favorable outcomes for both Jack and Bethany is given by:
5 * 2 = 10
Now, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes.
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 10 / 132
Simplifying the fraction:
Probability = 5 / 66
Since none of the given answer choices matches this probability, we need to find an equivalent fraction that does.
Multiplying the numerator and denominator by 2:
Probability = (5 * 2) / (66 * 2)
Probability = 10 / 132
Thus, the probability that Jack gets a peach and Bethany gets an orange is 10/132 which is equivalent to 5/66.
Therefore, none of the answer choices provided is correct.