SOLUTION: You have a pot with 100 balls. 20 of them are red, 50 are blue and 30 are green. You decide to draw 5 balls from the pot without replacement (i.e. you don't put a ball back in the
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-> SOLUTION: You have a pot with 100 balls. 20 of them are red, 50 are blue and 30 are green. You decide to draw 5 balls from the pot without replacement (i.e. you don't put a ball back in the
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Question 1019075: You have a pot with 100 balls. 20 of them are red, 50 are blue and 30 are green. You decide to draw 5 balls from the pot without replacement (i.e. you don't put a ball back in the pot once it has been taken out). What is the probability of drawing five blue balls?
Give your answer to 3 decimal places. Found 2 solutions by Fombitz, mathmate:Answer by Fombitz(32388) (Show Source):
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Question:
You have a pot with 100 balls. 20 of them are red, 50 are blue and 30 are green. You decide to draw 5 balls from the pot without replacement (i.e. you don't put a ball back in the pot once it has been taken out). What is the probability of drawing five blue balls?
Give your answer to 3 decimal places.
Solution:
The probability of drawing 5 blue balls is given by the product rule, namely the probability of having success in all five steps is the product of the probabilities of success in each step.
Step 1: P(B)=50/100
Step 2: P(B)=49/99 (49 blue balls left out of 99 remaining, i.e. no replacement)
Step 3: P(B)=48/98
Step 4: P(B)=47/97
Step 5: P(B)=46/96
Now multiply together the probabilities of each step.
P(BBBBB)=
=
=0.0281 (approximately)
This problem can also be solved using the Hypergeometric distribution, which gives
P(BBBBB)=C(50,5)*C(50,0)/C(100,5)= as before.
