13. A store sells a box of highlighters that contains 4 yellow, 3 blue, 2 pink, and 1 green highlighter. What is the probability of randomly picking first 1 blue and then 1 pink highlighter from the box without replacing the blue highlighter?
Q. 13. A store sells a box of highlighters that contains 4 yellow, 3 blue, 2 pink, and 1 green highlighter. What is the probability of randomly picking first 1 blue and then 1 pink highlighter from the box without replacing the blue highlighter?
Determine total highlighters: Determine the total number of highlighters in the box.The box contains 4 yellow, 3 blue, 2 pink, and 1 green highlighter. To find the total, we add these numbers together.4 yellow +3 blue +2 pink +1 green 3132 highlighters in total.
Calculate probability of blue: Calculate the probability of picking 1 blue highlighter first.The probability of an event is the number of favorable outcomes divided by the total number of outcomes. There are 3 blue highlighters and 10 highlighters in total.Probability of picking a blue highlighter first = Number of blue highlighters / Total number of highlighters = 103.
Determine new total highlighters: Determine the new total number of highlighters after picking 1 blue highlighter.After picking one blue highlighter, we do not replace it, so the total number of highlighters in the box is now 9.
Calculate probability of pink: Calculate the probability of picking 1 pink highlighter after picking a blue one.Now, there are 2 pink highlighters left and 9 highlighters in total.Probability of picking a pink highlighter after picking a blue one = Number of pink highlighters / New total number of highlighters = 92.
Calculate combined probability: Calculate the combined probability of both events happening consecutively.To find the combined probability of two independent events happening one after the other, we multiply the probabilities of each event.Combined probability = Probability of first event × Probability of second event = (103)×(92).
Perform final multiplication: Perform the multiplication to find the final probability.(3/10)×(2/9)=6/90.This fraction can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 6.6/90=1/15.
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