Question

in a class of 30 students, 12 walks to school, 10 travel by bus, 6 cycle and 2 travel by car.if 4 students is selected at random, find probability that
i. they all travel by the same means
ii.none of students cycle to school

Answer 1

\[P(all\ walk)=\frac{12C4}{30C4}\ ..........(1)\]
\[P(all\ bus)=\frac{10C4}{30C4}\ ...........(2)\]
\[P(all\ cycle)=\frac{6C4}{30C4}\ ..........(3)\]
\[P(all\ four\ go\ by\ car)=0\ .......(4)\]
To find the probability that all four travel by the same means, you need to add the values of probability found from equations (1), (2), (3) and (4).

Answer 2

@aiskarl Do you follow or do you need more explanation?

Answer 3

for the same means,i have to add eq 1,2,3,4 right? its means by no one selected to go by car?

Answer 4

The probability that all four students travel by car is zero, the reason being that only two students travel by car. Therefore zero is added to the total found by adding the values from equations 1, 2 and 3.

Answer 5

what if i just do (12C4+10C4+6C4)/(30C4)
??

Answer 6

Yes, that will give the correct result.

Answer 7

ii The probability that none of the four students selected at random cycles to school is found from:
\[P(n one\ of\ the\ four\ cycles)=\frac{24C4}{30C4}\]

Answer 8

I case you need to know how the calculate combinations, the value of 30C4 is found as follows:
\[30C4=\frac{30!}{4!(30-4)!}=\frac{30!}{4!26!}=\frac{30\times29\times28\times27}{4\times3\times2\times1}\]

Answer 9

how to calculate*

Answer 10

FOR NONE OF STUDENT CYCLE TO SCHOOL...:
(6C0)/(30C4)??

Answer 11

To find the probability that none of the four students cycles to school the equation is as follows:
\[P(none\ of\ the\ four\ cycles)=\frac{6C0\times24C4}{30C4}=\frac{24C4}{30C4}\]

Answer 12

IF 10 STUDENT ARE SELECTED AT RANDOM , FIND THE PROBABILITY THAT AT LEAST 6 STUDENT WALK TO SCHOOL AND AT LEAST CYCLE...

Answer 13

Note that 6C0 = 1

Answer 14

(6C4)+(7c3)+( 8C2) DIVIDE (30c10)

Answer 15

IS IT RIGHT MY ANSWER FOR MY NEW QUESTION?

Answer 16

You posted
"IF 10 STUDENT ARE SELECTED AT RANDOM , FIND THE PROBABILITY THAT AT LEAST 6 STUDENT WALK TO SCHOOL AND AT LEAST CYCLE..."
Please post the full question. I cannot comment on your answer until I have the full question.

Answer 17

CONTINUED FROM THIS QUESTION BUT NOT IN (i) AND (ii)

Answer 18

in a class of 30 students, 12 walks to school, 10 travel by bus, 6 cycle and 2 travel by car.
IF 10 STUDENT ARE SELECTED AT RANDOM , FIND THE PROBABILITY THAT AT LEAST 6 STUDENT WALK TO SCHOOL AND AT LEAST 2 CYCLE

Answer 19

Thank you. I will comment soon.

Answer 20

IF 10 STUDENT ARE SELECTED AT RANDOM , FIND THE PROBABILITY THAT AT LEAST 6 STUDENT WALK TO SCHOOL AND AT LEAST 2 CYCLE
The required probability is given by:
\[\frac{6C2(12C6+12C7+12C8)+12C6(6C3+6C4)}{30C10}\]