1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Murrr4er [49]
3 years ago
13

In a certain Algebra 2 class of 29 students, 7 of them play basketball and 24 of them play baseball. There are 3 students who pl

ay neither sport. What is the probability that a student chosen randomly from the class plays both basketball and baseball?
Mathematics
1 answer:
antiseptic1488 [7]3 years ago
6 0

Answer:

\frac{5}{29}

Step-by-step explanation:

Let n(A) represent students playing basketball, n(B) represent students playing baseball.

Then, n(A)=7, n(B)=24

Let n(S) be the total number of students. So, n(S)=29.

Now,

P(A)=\frac{n(A)}{n(S)}=\frac{7}{29}

P(B)=\frac{n(B)}{n(S)}=\frac{24}{29}

3 students play neither of the sport. So, students playing either of the two sports is given as:

n(A\cup B)=n(S)-3\\n(A\cup B)=29-3=26

∴ P(A\cup B)=\frac{n(A\cup B)}{n(S)}=\frac{26}{29}

From the probability addition theorem,

P(A\cup B)=P(A)+P(B)-P(A\cap B)

Where, P(A\cap B) is the probability that a student chosen randomly from the class plays both basketball and baseball.

Plug in all the values and solve for P(A\cap B) . This gives,

\frac{26}{29}=\frac{7}{29}+\frac{24}{29}+P(A\cap B)\\\\\frac{26}{29}=\frac{7+24}{29}+P(A\cap B)\\\\\frac{26}{29}=\frac{31}{29}+P(A\cap B)\\\\P(A\cap B=\frac{31}{29}-\frac{26}{29}\\\\P(A\cap B=\frac{31-26}{29}=\frac{5}{29}

Therefore, the probability that a student chosen randomly from the class plays both basketball and baseball is \frac{5}{29}

You might be interested in
A student identification card consists
denis23 [38]

Answer:

\frac{1}{30240}

Step-by-step explanation:

Given

ID Card of 5 digits

Possibly Digits = {0,1...,9}

Required

Probability that a card has exact number 94213

First, we have o determine the total possible number of ID card numbers

Let the card number be represented by ABCDE

Given that repetition of digits is not allowed;

<em>A can be any of 10 digits</em>

<em>B can any of the remaining 9 digits</em>

<em>C can be any of the remaining 8 digits</em>

<em>D can be any of the remaining 7 digits</em>

<em>E can be any of the remaining 6 digits</em>

<em />

Total number of cards = 10 * 9 *8 * 7 * 6

Total = 30240

Provided that the card number is generated at random; each card number has the same probability of \frac{1}{30240}

Hence, the probability of having 94213 is \frac{1}{30240}

6 0
3 years ago
How to explain what comes next 1,2,2,3,3,3,4,4,4,4 for third graders?
lesya692 [45]
Next it would be 5,5,5,5,5. Because, when you go up one in numbers you also go up one the amount.
6 0
3 years ago
2.1.4 Practice: Adding Rational Numbers
galina1969 [7]

Answer:

4+(-6)+8+(-1)

Step-by-step explanation:

if she starts at 4 points and her first turn she cuts 6 trees then you can add a negative 6 which is the same as subtracting that 6 when she plants 8 add those points then for her last turn add a negative 1 which is the same as subtracting 1 and she should end up with 5 points.

6 0
2 years ago
Add the complex numbers: ​ ​(-3+4i)+(7-i)
Romashka [77]
The answer is (3i+4)
5 0
2 years ago
Can someone plz help me with this one problem plzzzzz!!!!
rodikova [14]

Answer:

the 1st graph

Step-by-step explanation:

7 0
3 years ago
Other questions:
  • Julia has $80. She wants to purchase a nail paint set for $16 ans earrings. She spends the rest of the money on earrings. Each p
    11·2 answers
  • What polynomial has roots of −5, −4, and 1
    15·1 answer
  • Name from least to greatest 60 miles per hour, 24 feet per second, 45 kilometers per hour.
    12·1 answer
  • For the following, write an equivalent expression in standard form: (5x2 + 6x - 2) + 4x (3x – 7).
    12·1 answer
  • Which rectangle is similar to a rectangle 4 inches wide and 8 inches long
    12·1 answer
  • Evaluating Quadratic Functions Using a Graph
    10·2 answers
  • Hey guys<br> If f(x)=5x^(4/3), then f'(8)=?<br> can you solve this for me with good explanation
    5·2 answers
  • Beth said the distance to school is 2.8 km. The actual distance is 3.5 km. What is the percent error
    6·1 answer
  • Select the correct answer which graph passes the vertical line test​
    6·2 answers
  • MARKING AS BRAINLIEST PLUS MANY POINTS
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!