Question
I destroyer has 20 pins for fountain pens 10 gel pens and 6 ball point pins what is the probability of randomly Tuesday shell pin replacing it and then choosing a fountain pen 1/10 1/2 7/10 1/5
Answers
GPT 3.5
To calculate the probability of randomly choosing a shell pin and then a fountain pen, we need to first find the total number of shell pins and fountain pens:
Total shell pins = 20 (given)
Total fountain pens = 20 (20 fountain pens + 10 gel pens + 6 ballpoint pens)
The probability of randomly choosing a shell pin first is:
P(choosing shell pin) = Number of shell pins / Total number of pins
P(choosing shell pin) = 20 / (20 + 10 + 6)
P(choosing shell pin) = 20 / 36
P(choosing shell pin) = 5 / 9
Now, after choosing a shell pin, the probability of randomly choosing a fountain pen is:
P(choosing fountain pen) = Number of fountain pens / Total number of remaining pins
P(choosing fountain pen) = 20 / (36 - 1)
P(choosing fountain pen) = 20 / 35
P(choosing fountain pen) = 4 / 7
Therefore, the overall probability of randomly choosing a shell pin and then a fountain pen is:
P(choosing shell pin and fountain pen) = P(choosing shell pin) * P(choosing fountain pen)
P(choosing shell pin and fountain pen) = (5/9) * (4/7)
P(choosing shell pin and fountain pen) = 20 / 63
P(choosing shell pin and fountain pen) ≈ 0.317
Therefore, the probability of randomly choosing a shell pin and then choosing a fountain pen is approximately 0.317, which is equivalent to 31.7%.
So, the correct answer is not one of the options given.
Total shell pins = 20 (given)
Total fountain pens = 20 (20 fountain pens + 10 gel pens + 6 ballpoint pens)
The probability of randomly choosing a shell pin first is:
P(choosing shell pin) = Number of shell pins / Total number of pins
P(choosing shell pin) = 20 / (20 + 10 + 6)
P(choosing shell pin) = 20 / 36
P(choosing shell pin) = 5 / 9
Now, after choosing a shell pin, the probability of randomly choosing a fountain pen is:
P(choosing fountain pen) = Number of fountain pens / Total number of remaining pins
P(choosing fountain pen) = 20 / (36 - 1)
P(choosing fountain pen) = 20 / 35
P(choosing fountain pen) = 4 / 7
Therefore, the overall probability of randomly choosing a shell pin and then a fountain pen is:
P(choosing shell pin and fountain pen) = P(choosing shell pin) * P(choosing fountain pen)
P(choosing shell pin and fountain pen) = (5/9) * (4/7)
P(choosing shell pin and fountain pen) = 20 / 63
P(choosing shell pin and fountain pen) ≈ 0.317
Therefore, the probability of randomly choosing a shell pin and then choosing a fountain pen is approximately 0.317, which is equivalent to 31.7%.
So, the correct answer is not one of the options given.