SOLUTION: The table below shows the number of mangoes and cashew of the same size in a bag. If two of the fruits are picked at random, one at a time without replacement, find the probabili

Question 1184145: The table below shows the number of mangoes and cashew of the
same size in a bag. If two of the fruits are picked at random, one at a
time without replacement, find the probability that:
a. Both are good fruits b. Both are bad fruits
c. One is a good cashew and the other bad mango.
Mangoes Cashews Total
Good 10 6 18
Bad 6 8 12
Total 16 14 30
Found 2 solutions by CPhill, ikleyn:
Answer by CPhill(1959) (Show Source): You can put this solution on YOUR website!
Here's how to calculate the probabilities:
**a. Both are good fruits:**
* **First pick:** There are 18 good fruits out of a total of 30 fruits. The probability of picking a good fruit first is 18/30.
* **Second pick:** After picking one good fruit, there are now 17 good fruits left and a total of 29 fruits. The probability of picking another good fruit is 17/29.
* **Probability of both good:** Multiply the probabilities of each pick: (18/30) * (17/29) = 306/870 = 51/145 ≈ 0.3517
**b. Both are bad fruits:**
* **First pick:** There are 12 bad fruits out of 30 total fruits. The probability of picking a bad fruit first is 12/30.
* **Second pick:** After picking one bad fruit, there are 11 bad fruits left and 29 total fruits. The probability of picking another bad fruit is 11/29.
* **Probability of both bad:** Multiply the probabilities: (12/30) * (11/29) = 132/870 = 22/145 ≈ 0.1517
**c. One is a good cashew and the other a bad mango:**
There are two ways this can happen: good cashew then bad mango, or bad mango then good cashew. We have to calculate the probability of each case and then add them together.
* **Good cashew then bad mango:**
* Probability of good cashew first: 6/30
* Probability of bad mango second: 6/29
* Combined probability: (6/30) * (6/29) = 36/870 = 6/145 ≈ 0.0414
* **Bad mango then good cashew:**
* Probability of bad mango first: 6/30
* Probability of good cashew second: 6/29
* Combined probability: (6/30) * (6/29) = 36/870 = 6/145 ≈ 0.0414
* **Total probability:** Add the probabilities of the two scenarios: (6/145) + (6/145) = 12/145 ≈ 0.0828

Answer by ikleyn(52778) (Show Source): You can put this solution on YOUR website!
.
The table below shows the number of mangoes and cashew of the
same size in a bag. If two of the fruits are picked at random, one at a
time without replacement, find the probability that:
a. Both are good fruits b. Both are bad fruits
c. One is a good cashew and the other bad mango.

Mangoes Cashews Total Good 10 6 18 Bad 6 8 12 Total 16 14 30

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.
I am looking in your Table in the post, and I am scared.

In the first line (named 'Good'), the Table shows 10 mangoes, 6 Cashew and 18 Total.
It contradicts to my understanding that 10 + 6 = 16, so the Total in this line should be 16, not 18.

In the second line (named 'Bad'), the Table shows 6 mangoes, 8 Cashew and 12 Total.
It contradicts to my understanding that 6 + 8 = 14, so the Total in this line should be 14, not 12.

Please pass a message from me to the problem's creator, that he should learn
counting before creating math problems and disseminating them in the Internet.

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