A bag contain 10 oranges and 5 mangoes. Two fruits are drawn at random without replacement,what is the probability that the second fruit is a mango given that the first was an orange?
So you got your orange, leaving 14 fruits remaining.
prob(mango) = 5/14
To find the probability that the second fruit drawn is a mango given that the first fruit was an orange, we can use conditional probability.
To begin, let's calculate the probability of drawing an orange as the first fruit. Since there are 10 oranges out of a total of 15 fruits in the bag, the probability of drawing an orange as the first fruit is:
P(First fruit is an orange) = 10/15 = 2/3
After drawing the first fruit and without replacement, there are now 14 remaining fruits in the bag, including 5 mangoes. Therefore, the probability of drawing a mango as the second fruit, given that the first fruit was an orange, can be calculated as:
P(Second fruit is a mango | First fruit is an orange) = (Number of mangoes remaining) / (Total number of remaining fruits)
P(Second fruit is a mango | First fruit is an orange) = 5/14
So, the probability that the second fruit drawn is a mango given that the first fruit was an orange is 5/14.