Official Quant thread for CAT 2013

MBA CAT 2024
15203
@bs0409 said:
In a room there are 7 persons . the chance that two of them were born on the same day of the week?
Is it 2160/7^5??
2 ppl can be chosen in -> 7c2 ways
a day can be chosen in -> 7c1 ways
person 1 to be born on the selected day -> 1/7
person 2 to be born on the selected day -> 1/7
person 3 has -> 6/7
person 4 -> 5/7
person 5 -> 4/7
person 6 -> 3/7
person 7 -> 2/7
hence, total = (7c1*7c2*1/7*1/7*6/7*5/7*4/7*3/7*2/7) = 2160/7^5
15204
@bs0409 said:
In a room there are 7 persons . the chance that two of them were born on the same day of the week?
2160/(7^5) (Birthday Problem)
15205
@bs0409
2160/7^5
15206
http://en.wikipedia.org/wiki/Birthday_problem (article on birthday Problem)
15207
@shattereddream said:
http://en.wikipedia.org/wiki/Birthday_problem (article on birthday Problem)
thanks...this was cool... 😃
15208
A fair coin is tossed 10 times. Find the probability that the two heads do not occur consecutively?
a. 1/16b. 1/8c. 1/32d. None
15209
@ishu1991 said:
A fair coin is tossed 10 times. Find the probability that the two heads do not occur consecutively? a. 1/16b. 1/8c. 1/32d. None
Is it none??
all tails -> 1 case
1 head -> 10 cases
2 heads -> 9c2 = 36 cases
3 heads -> 8c3 = 56 cases
4 heads -> 7c4 = 35 cases
5 heads -> 6c5 = 6 cases
total = 144
hence, prob = 144/2^10 = 9/2^6
15210
@Logrhythm
15211

"The average of all students who score more than 70% marks in 74%. The average of all students who scored more than equal to 60% is 68%. Of the students scoring more than or equal to 60%, at least what percent of students scored between 60% and 70%."

15212
@ishu1991 said:
A fair coin is tossed 10 times. Find the probability that the two heads do not occur consecutively? a. 1/16b. 1/8c. 1/32d. None
D. None (Application of fibonacci ) Arun Sharma ka hai kya ye problem . Arun Sharma's Probability problems are good love this chapter of arun sharma
15213
@shattereddream
han bhai unhi ka hain
15214
@veertamizhan said:
"The average of all students who score more than 70% marks in 74%. The average of all students who scored more than equal to 60% is 68%. Of the students scoring more than or equal to 60%, at least what percent of students scored between 60% and 70%."
Is it 62% ??
15215
@doctoriim nahi 43.84
15216
@veertamizhan said:
A milkman mixes 20 liters of water with 80 lts of milk. After selling 1/4th of the mixture, he adds water to replenish the quantity he has sold. What is the current proportion of water to milk?
2:3 ?
15217
@doctoriim yes
15218
@ishu1991 said:
A fair coin is tossed 10 times. Find the probability that the two heads do not occur consecutively? a. 1/16b. 1/8c. 1/32d. None
Sample Space = 2^10

Now, Heads won't be consecutive if there will be less than or equal to 5 heads appearing.

So, 0 Head => 1 way.
1 Head => 10 ways.
2 Heads => 9C2 = 36 ways.
3 Heads => 8C3 = 56 ways.
4 Heads => 7C4 = 35 ways.
5 Heads => 6C5 = 6 ways.

Total Ways = 11 + 92 + 41 = 144 ways.

Thus, Probability = 144/2^10 = 9/2^6 [Opton D - None].
15219
@ishu1991 said:
A fair coin is tossed 10 times. Find the probability that the two heads do not occur consecutively? a. 1/16b. 1/8c. 1/32d. None
typical application of fibonacci series .. Look for 10th fibonacci number , you are done

2,3,5,8,13,21,34,55,89,144

144/1024 ..
15220
@naga25french said:
typical application of fibonacci series .. Look for 10th fibonacci number , you are done

2,3,5,8,13,21,34,55,89,144

144/1024 ..
But buddy the Fibonacci series starts from 0 1 1 2 3 5 8 13 21 34 55 89 144...so how can be the 10th number be 144??
15221
@saurav5517 said:
But buddy the Fibonacci series starts from 0 1 1 2 3 5 8 13 21 34 55 89 144...so how can be the 10th number be 144??
if the first toss is heads , second toss cannot be heads .

so heads can occur from 3rd toss and tails from second toss ..

so 2,3,5....

by fibonacci series , I didnt mean normal series which we use .. we need to modify the series based on req .

Tweaked version of it :

You have staircase with 10 steps . You can climbs either one or two steps at a time .. In how many ways you can reach the top of staircase ?
15222
@naga25french said:
if the first toss is heads , second toss cannot be heads .

so heads can occur from 3rd toss and tails from second toss ..

so 2,3,5....

by fibonacci series , I didnt mean normal series which we use .. we need to modify the series based on req .

Tweaked version of it :

You have staircase with 10 steps . You can climbs either one or two steps at a time .. In how many ways you can reach the top of staircase ?
Now if the first toss is tails , second toss can be heads ..
So tails can occur from 3rd toss and heads from the second toss..
Shall the logic be the same??