Solve the following problems: 1) Out of the 45 books in the bookshelves, 18 are mathematics books, 10 are science books, 9 are history books and 8 are story books. If you pick one book at random, what is the probability that it is a science or mathematics book? 2) In a particular class, 78% of the students have a smartphone, 38% have a smartphone and a tablet, and 3 % have neither a smartphone nor a tablet. Find the probability that a randomly selected student has a a) tablet? b) tablet or a smartphone? c) smartphone but does not have a tablet? 3) In a junior high school completing class of 510 students, 110 are on the Science, Technology and Engineering (STE) Program. Of these, 78 of the STE Program students and 112 of the non-STE program students will take
1. Solve the following problems: 1) Out of the 45 books in the bookshelves, 18 are mathematics books, 10 are science books, 9 are history books and 8 are story books. If you pick one book at random, what is the probability that it is a science or mathematics book? 2) In a particular class, 78% of the students have a smartphone, 38% have a smartphone and a tablet, and 3 % have neither a smartphone nor a tablet. Find the probability that a randomly selected student has a a) tablet? b) tablet or a smartphone? c) smartphone but does not have a tablet? 3) In a junior high school completing class of 510 students, 110 are on the Science, Technology and Engineering (STE) Program. Of these, 78 of the STE Program students and 112 of the non-STE program students will take
Answer:
1.) 8/45
2.) a) 47/100, b) 77/100, c) 4/5
3.) a) 78/510, b) 22/85, c) 26/85
Step-by-step explanation:
1.) The probability of picking a mathematics book is 18/45 = 2/5. The probability of picking a science book is 10/45 = 2/9.
To find the probability of picking a science or mathematics book, we add the probabilities of picking a mathematics book and a science book and subtract the probability of picking a book that is both a mathematics and a science book (which is 0):
P(science or mathematics book) = P(mathematics book) + P(science book) - P(mathematics and science book)
= 2/5 + 2/9 - 0
= 28/45
Therefore, the probability of picking a science or mathematics book is 28/45.
2.) Let S and T be the events that a student has a smartphone and a tablet, respectively. Then, the probability of a student having a smartphone is 78/100 = 39/50, and the probability of a student having neither a smartphone nor a tablet is 3/100.
a) The probability of a student having a tablet is P(T) = P(S and T) + P(not S and T). We know that P(S and T) = 38/100 = 19/50, and the probability of a student having a tablet but not a smartphone is P(not S and T).
P(not S and T) = P(T) - P(S and T)
= 19/50 - 38/100
= 13/100
Therefore, the probability of a randomly selected student having a tablet is 19/50 + 13/100 = 47/100.
b) The probability of a student having either a smartphone or a tablet is P(S or T) = P(S) + P(T) - P(S and T).
P(S or T) = 39/50 + 47/100 - 19/50
= 77/100
Therefore, the probability of a randomly selected student having either a smartphone or a tablet is 77/100.
c) The probability of a student having a smartphone but not a tablet is P(S and not T) = P(S) - P(S and T).
P(S and not T) = 39/50 - 19/50
= 4/5
Therefore, the probability of a randomly selected student having a smartphone but not a tablet is 4/5.
3.) Let S be the event that a student is in the STE program, and T be the event that a student will take the advanced mathematics course. Then, we are given that P(S) = 110/510, P(T|S) = 78/110, and P(T|not S) = 112/400.
a) The probability of a randomly selected student being in the STE program and taking the advanced mathematics course is:
P(S and T) = P(T|S) * P(S)
= (78/110) * (110/510)
= 78/510
b) The probability of a randomly selected student taking the advanced mathematics course is:
P(T) = P(T|S) * P(S) + P(T|not S) * P(not S)
= (78/110) * (110/510) + (112/400) * (400/510)
= (78/510) + (28/255)
= 22/85
c) The probability of a randomly selected student taking the advanced mathematics course given that they are in the STE program is:
P(T|S) = P(S and T) / P(S)
= (78/510) / (110/510)
= 26/85
Therefore, the probability of a randomly selected student in the STE program taking the advanced mathematics course is 26/85.
