A basket of fruits contains 5 bananas, 8 mangoes, and 7 apples. Two fruits are randomly selected without replacement. Calculate the probability of selecting an apple and a banana.(1 point)
Responses
35
, Start Fraction 3 over 5 End Fraction
780
, Start Fraction 7 over 80 End Fraction
21190
, Start Fraction 21 over 190 End Fraction
776
To calculate the probability of selecting an apple and a banana from the basket, we need to determine the total number of possible outcomes and the number of favorable outcomes.
The total number of fruits in the basket is 5 + 8 + 7 = 20.
To select the first fruit, we have 20 options.
After selecting the first fruit, there will be 19 fruits left in the basket.
To select the second fruit, we have 19 options.
The total number of possible outcomes is 20 * 19 = 380.
To calculate the number of favorable outcomes, we can focus on selecting an apple and a banana.
The number of apples in the basket is 7, so we have 7 options for selecting an apple.
After selecting an apple, there will be 19 fruits left in the basket, including 5 bananas.
The number of bananas in the remaining fruits is 5, so we have 5 options for selecting a banana.
The number of favorable outcomes is 7 * 5 = 35.
Therefore, the probability of selecting an apple and a banana is 35/380.
Simplifying the fraction, we get 7/76.
So, the correct answer is "Start Fraction 7 over 76 End Fraction".
To calculate the probability of selecting an apple and a banana, we need to first find the total number of possible outcomes. Since two fruits are randomly selected without replacement, there are a total of (5+8+7) 20 fruits to choose from for the first selection, and then (20-1) 19 fruits remaining for the second selection.
The number of ways to select an apple and a banana can be calculated by multiplying the number of apples (7) by the number of bananas (5).
Therefore, the probability of selecting an apple and a banana is:
(7/20) * (5/19)
Simplifying this expression gives us:
35/380
So, the correct answer is:
Start Fraction 35 over 380 End Fraction