Classroom

Of the 26 pupils in the classroom, 12 boys and 14 girls, four representatives are picked to the odds of being:
a) all the girls
b) three girls and one boy
c) there will be at least two boys

Correct result:

p₁ =  0.067
p₂ =  0.2922
p₃ =  0.6409

Solution:

$p_1={\displaystyle \frac{14\cdot 13\cdot 12\cdot 11}{26\cdot 25\cdot 24\cdot 23}}={\displaystyle \frac{77}{1150}}=0.067$

$$\begin{gathered} C_3(14)=\left({\displaystyle \genfrac{}{}{0px}{}{14}{3}}\right)={\displaystyle \frac{14!}{3!(14-3)!}}={\displaystyle \frac{14\cdot 13\cdot 12}{3\cdot 2\cdot 1}}=364 \\ {C}_1(12)=\left({\displaystyle \genfrac{}{}{0px}{}{12}{1}}\right)={\displaystyle \frac{12!}{1!(12-1)!}}={\displaystyle \frac{12}{1}}=12 \\ {C}_4(26)=\left({\displaystyle \genfrac{}{}{0px}{}{26}{4}}\right)={\displaystyle \frac{26!}{4!(26-4)!}}={\displaystyle \frac{26\cdot 25\cdot 24\cdot 23}{4\cdot 3\cdot 2\cdot 1}}=14950 \\ {p}_2=\left(\genfrac{}{}{0px}{}{14}{3}\right)\cdot \left(\genfrac{}{}{0px}{}{12}{1}\right)\mathrm{/}\left(\genfrac{}{}{0px}{}{26}{4}\right)=364\cdot 12\mathrm{/}14950={\displaystyle \frac{168}{575}}=0.2922 \end{gathered}$$

$p_3=1-p_1-p_2=1-0.067-0.2922={\displaystyle \frac{737}{1150}}=0.6409$

Try another example

Showing 0 comments:

Next similar math problems:

• Boys and girls
  There are eight boys and nine girls in the class. There were six children on the trip from this class. What is the probability that left a) only boys b) just two boys
• School parliament
  There are 18 boys and 14 girls in the class. In how many ways can 3 representatives be elected to the school parliament, if these are to be: a) the boys themselves b) one boy and two girls
• Boys and girls
  There are 11 boys and 18 girls in the classroom. Three pupils will answer. What is the probability that two boys will be among them?
• Graduation party
  There are 15 boys and 12 girls at the graduation party. Determine how many four couples can be selected.
• Peaches
  There are 20 peaches in the pocket. 3 peaches are rotten. What is the probability that one of the randomly picked two peaches will be just one rotten?
• In the classroom
  There are 30 boys and a few girls in the class. In the six months, 28 boys and all girls benefited, which was 95% of all pupils. How many pupils are there in the classroom?
• Four-member team
  There are 14 girls and 11 boys in the class. How many ways can a four-member team be chosen so that there are exactly two boys in it?
• Families 2
  Seven hundred twenty-nine families are having six children each. The probability of a girl is 1/3, and the probability of a boy is 2/3. Find the number of families having two girls and four boys.
• Competition
  15 boys and 10 girls are in the class. On school competition of them is selected 6-member team composed of 4 boys and 2 girls. How many ways can we select students?
• Desks
  A class has 20 students. The classroom consists of 20 desks, with 4 desks in each of 5 different rows. Amy, Bob, Chloe, and David are all friends, and would like to sit in the same row. How many possible seating arrangements are there such that Amy, Bob,
• Boys and girls
  There are 20 boys and 10 girls in the class. How many different dance pairs can we make of them?
• Girls
  The boys and girls in the class formed without the rest of the fives, 2 girls and 3 boys. There are 6 girls missing to create mixed pairs (1 boy and 1 girl). How many girls are in the classroom?
• Family
  94 boys are born per 100 girls. Determine the probability that there are two boys in a randomly selected family with three children.
• Pairs
  From the five girls and four boys teachers have to choose one pair of boy and girl. A) How many such pairs of (M + F)? B) How many pairs where only boys (M + M)? C) How many are all possible pairs?
• Research in school
  For particular research in high school, four pupils are to be selected from a class with 30 pupils. Calculate the number of all possible results of the select and further calculate the number of all possible results, if it depends on the order in which th
• Six questions test
  There are six questions in the test. There are 3 answers to each - only one is correct. In order for a student to take the exam, at least four questions must be answered correctly. Alan didn't learn at all, so he circled the answers only by guessing. What
• Raffle
  There are 200 draws in the raffle, but only 20 of them win. What is the probability of at least 4 winnings for a group of people who have bought 5 tickets together?