A box containing 2 red pencils, 3 yellow pencils, 4 green pencils and 1 blue pencil.Two pencils are drawn at random without replacement. What is the probability of picking a yellow pencil on the first draw and a red pencil on the second draw?Responses 1151 over 15 5195 over 19
Question
A box containing 2 red pencils, 3 yellow pencils, 4 green pencils and 1 blue pencil.Two pencils are drawn at random without replacement. What is the probability of picking a yellow pencil on the first draw and a red pencil on the second draw?Responses 1151 over 15 5195 over 19
Solution
To solve this problem, we need to calculate the probability of each event separately and then multiply them together because these are independent events.
Step 1: Calculate the total number of pencils: 2 red + 3 yellow + 4 green + 1 blue = 10 pencils
Step 2: Calculate the probability of drawing a yellow pencil first: There are 3 yellow pencils out of a total of 10, so the probability is 3/10.
Step 3: Calculate the probability of drawing a red pencil second: After drawing a yellow pencil, there are now 9 pencils left. Of these, 2 are red. So the probability is 2/9.
Step 4: Multiply the probabilities together: (3/10) * (2/9) = 6/90 = 1/15.
So, the probability of drawing a yellow pencil first and a red pencil second is 1/15.
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