There are 12 mangoes in a bag, out of which 4 are not ripe. If 5 mangoes are taken out of the bag randomly, what is the probability of selecting only ripen mangoes?7/998/999/9910/9911/99
Question
There are 12 mangoes in a bag, out of which 4 are not ripe. If 5 mangoes are taken out of the bag randomly, what is the probability of selecting only ripen mangoes?7/998/999/9910/9911/99
Solution
To solve this problem, we need to use the concept of probability.
Step 1: Identify the total number of mangoes and the number of ripe mangoes. There are 12 mangoes in total and 4 of them are not ripe. So, the number of ripe mangoes is 12 - 4 = 8.
Step 2: Calculate the total number of ways to select 5 mangoes out of 12. This can be calculated using the combination formula, C(n, r) = n! / [(n-r)! * r!], where n is the total number of items, r is the number of items to choose, and '!' denotes factorial. So, the total number of ways to select 5 mangoes out of 12 is C(12, 5) = 12! / [(12-5)! * 5!] = 792.
Step 3: Calculate the number of ways to select 5 ripe mangoes out of 8. Using the same combination formula, the number of ways to select 5 ripe mangoes out of 8 is C(8, 5) = 8! / [(8-5)! * 5!] = 56.
Step 4: Calculate the probability of selecting only ripe mangoes. The probability is the number of favorable outcomes divided by the total number of outcomes. So, the probability of selecting only ripe mangoes is 56 / 792 = 0.070707...
So, the probability of selecting only ripe mangoes when 5 mangoes are taken out randomly from the bag is approximately 0.07 or 7%.
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