A basket contains 80 mangoes and 60 oranges.if two fruits are picked one after the other without replacement,what is the probability that
1) one of each fruit is picked
2) one type of fruit is picked
without replacement?
Pr(one mango, one orange)=80/140*69/140*2
pr(two mangoes, or two oranges)
= 80/140*80/140 + 60/140*60/140
To find the probability in each case, we need to determine the total number of possibilities and the number of favorable outcomes.
1) Probability of picking one of each fruit:
Total number of possibilities = (80 + 60) = 140 fruits
Number of favorable outcomes = (80 * 60) = 4800 (picking one mango and one orange)
Probability = Number of favorable outcomes / Total number of possibilities
Probability = 4800 / 140 = 34.29%
Therefore, the probability of picking one of each fruit is approximately 34.29%.
2) Probability of picking one type of fruit:
In this case, we can either pick one mango or one orange.
a) Picking one mango:
Total number of possibilities = (80 + 60) = 140 fruits
Number of favorable outcomes = 80 (picking one mango)
Probability = Number of favorable outcomes / Total number of possibilities
Probability = 80 / 140 = 57.14%
b) Picking one orange:
Total number of possibilities = (80 + 60) = 140 fruits
Number of favorable outcomes = 60 (picking one orange)
Probability = Number of favorable outcomes / Total number of possibilities
Probability = 60 / 140 = 42.86%
Therefore, the probability of picking one type of fruit (either mango or orange) is approximately 57.14% or 42.86%, depending on whether you select mango or orange.
Please note that these probabilities are based on the assumption that the fruits are well mixed and each fruit has an equal chance of being picked.
To find the probability of these events, we need to determine the total number of possible outcomes and the favorable outcomes.
1) Probability of picking one of each fruit:
Total possible outcomes when picking two fruits without replacement = (80 + 60) × (80 + 60 - 1). This is because we have 80 mangoes and 60 oranges, and we choose two fruits without replacement, so we multiply the total number of fruits by one less than the total number of fruits.
Favorable outcomes: We need to choose one mango and one orange. The number of ways to choose one mango is 80, and the number of ways to choose one orange is 60.
Probability = (Number of Favorable Outcomes) / (Total Possible Outcomes)
= (80 × 60) / [(80 + 60) × (80 + 60 - 1)]
2) Probability of picking only one type of fruit:
Total possible outcomes when picking two fruits without replacement = (80 + 60) × (80 + 60 - 1).
Favorable outcomes: We can either choose two mangoes or two oranges. There are 80 ways to choose two mangoes and 60 ways to choose two oranges.
Probability = (Number of Favorable Outcomes) / (Total Possible Outcomes)
= (80 + 60) / [(80 + 60) × (80 + 60 - 1)]
To calculate the exact probabilities, you can simplify the fractions and perform the division.