I need someone to tell me how to set these up please?
1. A box contains 4 quarters. 2 of the quarters have the American eagle on the back. Suppose you draw 2 quarters at random with replacement.
a. What's the probability that both have the American eagle on the back?
b. What's the probability that neither have the American eagle?
c. What's the probability that AT LEAST one has the American eagle?
2. In a survey, 28% of students said they were left-handed. 64% said they were right-handed and 8% said they were ambidextrous. If you omitted the ambidestrous people, what percent of the students remaining are left-handed?
3. 75% of boys like hockey. 65% of girls like hockey. There are an equal number of boys and girls. If someone does not like hockey, what's the probability that it's a boy?
1.
Let E be 'eagle on back"
let N be 'not eagle on back'
There are only 4 possible outcomes
EE, NE, EN, and NN
since there is replacement each of those above events has a prob of 1/4 from (2/4 x 2/4)
so a) is 2/4 x 2/4 = 1/4
b) NN or 1/4 again
c) is 1/4 + 1/4 = 1/2
3.
for conveniece sake, let's say there are 100 boys, then there are 100 girls or a total of 200
the number of boys who don't like hockey is 25
so prob that a boy doesn't like hockey = 25/200 = 1/8
do #2 the same way.
But you're taking the number of boys from the percent of people that don't like hockey. 60% of people don't like hockey. So it's 25%/60%, right? So, wouldn't it be 42%?
That's why I wanted you to pick an arbitrary number, I used 100 because it so convenient.
Can't we break down our 200 students into 4 categories.
boys who like hockey = 75
boys who don't like hockey = 25
girls who like hockey = 65
girls who don't like hockey = 35
(notice that totals 200)
prob(of some event) =number of cases in that event / total number of cases
our event is (boys who don't like hockey)
so prob = 25/200 = 1/8
I don't see how you can interpret that in any other way.
Sure, I can help you with these probability questions. To solve probability problems, we need to understand the basic principles and use relevant formulas.
1. Box containing 4 quarters with 2 having the American eagle on the back:
a. To find the probability that both quarters have the American eagle on the back, you need to calculate the probability of drawing the first quarter with the American eagle, and then multiply it by the probability of drawing the second quarter with the American eagle. Since you are drawing with replacement, the probability remains the same on multiple draws. So, the probability of drawing a quarter with the American eagle is 2/4 = 1/2. Therefore, the probability of drawing two quarters with the American eagle is (1/2) * (1/2) = 1/4.
b. The probability that neither quarter has the American eagle can be found by subtracting the probability of both quarters having the American eagle from 1. So, 1 - 1/4 = 3/4.
c. The probability of at least one quarter having the American eagle can be calculated by subtracting the probability of neither quarter having the American eagle from 1. So, the probability is 1 - 3/4 = 1/4.
2. In a survey:
Given that 28% of students are left-handed, 64% are right-handed, and 8% are ambidextrous, if we omit the ambidextrous people, we need to find the percentage of left-handed students out of the remaining respondents.
To do this, we need to calculate the percentage of students who are not ambidextrous, which is 100% - 8% = 92%.
Out of these remaining students, the percentage of left-handed students is 28% out of 92%. Simplifying this, we find that the percentage of left-handed students is (28/100) * 92 = 25.76%. Therefore, 25.76% of the remaining students are left-handed.
3. Given that 75% of boys like hockey, 65% of girls like hockey, and there are an equal number of boys and girls, we need to find the probability that someone who does not like hockey is a boy.
To do this, we need to calculate the percentage of boys who do not like hockey. Since we know that there are an equal number of boys and girls, the total percentage of people who do not like hockey is 100% - 75% = 25% for boys and 100% - 65% = 35% for girls.
To find the probability that someone who does not like hockey is a boy, we divide the percentage of boys who do not like hockey (25%) by the total percentage of people who do not like hockey (25% + 35%). Simplifying this, we find that the probability is (25% / (25% + 35%)) * 100 = 41.67%. Therefore, the probability that someone who does not like hockey is a boy is approximately 41.67%.
I hope this explanation helps you understand how to solve these probability problems. Let me know if you have any further questions!