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?

Question

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Solution 1

Step 1: Identify the total number of mangoes. In this case, it's 12.

Step 2: Identify the number of ripe mangoes. Since 4 are not ripe, we subtract 4 from 12 to get 8 ripe mangoes.

Step 3: Identify the number of mangoes being selected. In this case, it's 5.

Step 4: Calculate the probability of selecting only ripe mangoes. This is done by dividing the number of ways to select 5 ripe mangoes from 8 by the total number of ways to select 5 mangoes from 12.

The number of ways to select 5 ripe mangoes from 8 is calculated using combinations, denoted as C(n, r) where n is the total number of items, and r is the number of items to choose. So, C(8, 5) = 8! / [(8-5)! * 5!] = 56.

The total number of ways to select 5 mangoes from 12 is calculated as C(12, 5) = 12! / [(12-5)! * 5!] = 792.

So, the probability of selecting only ripe mangoes is 56 / 792 = 0.0707 or approximately 7.07%.

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Solution 2

Step 1: Identify the total number of mangoes. In this case, there are 12 mangoes.

Step 2: Identify the number of ripe mangoes. There are 12 total mangoes and 4 are not ripe, so there are 12 - 4 = 8 ripe mangoes.

Step 3: Identify the number of mangoes being selected. In this case, 5 mangoes are being selected.

Step 4: Calculate the probability of selecting only ripe mangoes. This is done by dividing the number of ways to select 5 ripe mangoes from 8 by the total number of ways to select 5 mangoes from 12.

The number of ways to select 5 ripe mangoes from 8 is calculated using combinations, which is denoted as C(n, r) where n is the total number of items, and r is the number of items to choose. So, the number of ways to select 5 ripe mangoes from 8 is C(8, 5).

Similarly, the total number of ways to select 5 mangoes from 12 is C(12, 5).

So, the probability of selecting only ripe mangoes is C(8, 5) / C(12, 5).

Step 5: Calculate the values of C(8, 5) and C(12, 5).

C(8, 5) = 8! / [5!(8-5)!] = 56 C(12, 5) = 12! / [5!(12-5)!] = 792

So, the probability of selecting only ripe mangoes is 56 / 792 = 0.0707 (rounded to four decimal places).

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Solution 3

Sure, here's how you can calculate the probability:

Step 1: Identify the total number of mangoes. In this case, it's 12.

Step 2: Identify the number of ripe mangoes. Since 4 are not ripe, there are 12 - 4 = 8 ripe mangoes.

Step 3: We want to find the probability of picking 5 ripe mangoes.

Step 4: The number of ways to pick 5 mangoes out of 8 ripe ones can be calculated using combinations. This is denoted as C(8,5).

Step 5: Similarly, the total number of ways to pick 5 mangoes out of 12 is C(12,5).

Step 6: The probability of picking 5 ripe mangoes is therefore C(8,5) / C(12,5).

Step 7: Calculate C(8,5) and C(12,5).

C(n, r) = n! / [r!(n-r)!]

So, C(8,5) = 8! / [5!(8-5)!] = 56 And, C(12,5) = 12! / [5!(12-5)!] = 792

Step 8: Substitute these values back into the probability formula to get the final answer.

Probability = C(8,5) / C(12,5) = 56 / 792 = 0.0707

So, the probability of selecting only ripe mangoes is approximately 0.0707 or 7.07%.

This problem has been solved

Solution 4

Step 1: Identify the total number of mangoes. In this case, it's 12.

Step 2: Identify the number of ripe mangoes. Since 4 are not ripe, we subtract 4 from 12 to get 8 ripe mangoes.

Step 3: Identify the number of mangoes being selected. In this case, it's 5.

Step 4: We need to find the probability of selecting 5 ripe mangoes. This is a combination problem, as the order of selection does not matter.

Step 5: The formula for combination is C(n, r) = n! / [r!(n-r)!], where n is the total number of items, r is the number of items to choose, and "!" denotes factorial.

Step 6: Calculate the total number of ways to select 5 mangoes from 12. Using the combination formula, C(12, 5) = 12! / [5!(12-5)!] = 792.

Step 7: Calculate the number of ways to select 5 ripe mangoes from 8. Using the combination formula, C(8, 5) = 8! / [5!(8-5)!] = 56.

Step 8: The probability of selecting 5 ripe mangoes is the number of ways to select 5 ripe mangoes divided by the total number of ways to select 5 mangoes. So, the probability = 56 / 792 = 0.0707.

So, the probability of selecting only ripe mangoes is approximately 0.0707 or 7.07%.

This problem has been solved

Solution 5

Step 1: Identify the total number of mangoes. In this case, it's 12.

Step 2: Identify the number of ripe mangoes. Since 4 are not ripe, we subtract 4 from 12 to get 8 ripe mangoes.

Step 3: Identify the number of mangoes being selected. In this case, it's 5.

Step 4: Calculate the probability of selecting only ripe mangoes. This is done by dividing the number of ways to choose 5 ripe mangoes from 8 by the total number of ways to choose 5 mangoes from 12.

The number of ways to choose 5 ripe mangoes from 8 is calculated using the combination formula, which is C(n, r) = n! / [r!(n-r)!], where n is the total number of items, r is the number of items to choose, and ! denotes factorial.

So, the number of ways to choose 5 ripe mangoes from 8 is C(8, 5) = 8! / [5!(8-5)!] = 56.

Similarly, the total number of ways to choose 5 mangoes from 12 is C(12, 5) = 12! / [5!(12-5)!] = 792.

So, the probability of selecting only ripe mangoes is 56 / 792 = 0.0707 or 7.07% when rounded to two decimal places.

This problem has been solved

Solution 6