luke put 2 red pens, 7 blue pens, and 1 black pen in a bag, closed it and shook it up. if the pens are the same size, weight and texture, what is the probally of choosing a red pen? a red or black pen? what is the probability of not choosing a blue pen? if luke does choose a blue pen, but gives it away, what is the probability he will choose another blue pen? i need help asap it is due tommrow
To find the probabilities in this scenario, we need to determine the total number of pens and the number of pens in each category.
Total number of pens = 2 red pens + 7 blue pens + 1 black pen = 10 pens
Probability of choosing a red pen:
Number of red pens = 2
Probability of choosing a red pen = Number of red pens / Total number of pens = 2/10 = 1/5
Probability of choosing a red or black pen:
Number of red pens + Number of black pens = 2 + 1 = 3
Probability of choosing a red or black pen = (Number of red pens + Number of black pens) / Total number of pens = 3/10
Probability of not choosing a blue pen:
Number of pens that are not blue = Number of red pens + Number of black pens = 2 + 1 = 3
Probability of not choosing a blue pen = (Number of pens that are not blue) / Total number of pens = 3/10
If Luke chooses a blue pen and gives it away, the total number of pens remaining reduces to 9 (2 red pens, 6 blue pens, and 1 black pen).
Probability of choosing another blue pen after giving away a blue pen:
Number of blue pens remaining = 6
Probability of choosing another blue pen = Number of blue pens remaining / Total number of remaining pens = 6/9 = 2/3
To summarize:
Probability of choosing a red pen: 1/5
Probability of choosing a red or black pen: 3/10
Probability of not choosing a blue pen: 3/10
Probability of choosing another blue pen after giving away a blue pen: 2/3
Remember to always double-check your work and adjust if any additional information or constraints are given in the problem.