Freshman
Satisfied=55
Neutral=21
Not satisfied=17
Total=93
Sophomore
Satisfied=49
Neutral=18
Not satisfied=15
Total=82
Junior
Satisfied=68
Neutral=14
Not satisfied=14
Total=96
Senior
Satisfied=63
Neutral=11
Not satisfied=22
Total=96
total Satisfied=235
total Neutral=64
total Not satisfied=68
total Total=367
If a survey participant is selected at random, what is the probability that he or she is satisfied or a junior?
P(satisfied or junior)=
formula : P(E or F)= P(E)+P(F)-P(E and F)
P(satisfied or junior) = P(satisfied) + P(junior) - P(satisfied and junior)
P(satisfied) = total satisfied / total participants = 235 / 367
P(junior) = total junior / total participants = 96 / 367
P(satisfied and junior) = satisfied and junior / total participants = 68 / 367
P(satisfied or junior) = 235 / 367 + 96 / 367 - 68 / 367
P(satisfied or junior) ≈ 0.639
Your answer is wrong. Use the General Addition Rule to find the probability. The rule states that for any two events E and F,
P(E or F)= P(E)+P(F)-P(E and F).
Apologies for the error. Let's use the General Addition Rule to find the probability.
P(satisfied or junior) = P(satisfied) + P(junior) - P(satisfied and junior)
P(satisfied) = total satisfied / total participants = 235 / 367
P(junior) = total junior / total participants = 96 / 367
P(satisfied and junior) = satisfied and junior / total participants = 68 / 367
P(satisfied or junior) = P(satisfied) + P(junior) - P(satisfied and junior)
P(satisfied or junior) = 235 / 367 + 96 / 367 - 68 / 367
P(satisfied or junior) = 329 / 367
P(satisfied or junior) ≈ 0.896
How did you got 329/367 I got 263/367
Apologies for the confusion. Let's calculate it again:
P(satisfied) = total satisfied / total participants = 235 / 367
P(junior) = total junior / total participants = 96 / 367
P(satisfied and junior) = satisfied and junior / total participants = 68 / 367
P(satisfied or junior) = P(satisfied) + P(junior) - P(satisfied and junior)
P(satisfied or junior) = 235 / 367 + 96 / 367 - 68 / 367
P(satisfied or junior) = 331 / 367
P(satisfied or junior) ≈ 0.9
To find the probability that a survey participant is satisfied or a junior, we need to calculate the individual probabilities and the probability of both events occurring at the same time.
1. Calculate the probability of being satisfied:
P(satisfied) = (total satisfied) / (total participants) = 235 / 367 ≈ 0.64
2. Calculate the probability of being a junior:
P(junior) = (total juniors) / (total participants) = 96 / 367 ≈ 0.26
3. Calculate the probability of being satisfied and a junior:
P(satisfied and junior) = (number of satisfied juniors) / (total participants) = (68/96) ≈ 0.71
4. Calculate the probability of being satisfied or a junior:
P(satisfied or junior) = P(satisfied) + P(junior) - P(satisfied and junior)
P(satisfied or junior) = 0.64 + 0.26 - 0.71 ≈ 0.19
Therefore, the probability that a survey participant is satisfied or a junior is approximately 0.19.
To find the probability that a survey participant selected at random is satisfied or a junior, we can use the formula:
P(E or F) = P(E) + P(F) - P(E and F)
Let's calculate the values necessary for this formula:
For Satisfied:
Total Satisfied = 235
Total Participants = 367
P(Satisfied) = Total Satisfied / Total Participants = 235 / 367
For Junior:
Total Junior = 96
Total Participants = 367
P(Junior) = Total Junior / Total Participants = 96 / 367
For Satisfied and Junior:
Total Satisfied and Junior = ?? (This information is not provided in the question)
Once you have the value for Total Satisfied and Junior, you can use the formula to calculate the probability:
P(Satisfied or Junior) = P(Satisfied) + P(Junior) - P(Satisfied and Junior)
Remember, to find the probability, you need the value for "Total Satisfied and Junior." Without that information, it is not possible to calculate the exact probability.