Adding one more:
What is the probability for a family with three children to have a boy and two girls, assuming the probability of having a boy or a girl is equal?
a)1/8
b)
c)
d)3/8
e)5/8
Probability of having a boy out of 3 children is P(b) * P(g) * P(g) =1/2 * 1/2 * 1/2 = 1/8
bgg is 1/8
gbg is 1/8
ggb is 1/8
So overall: 3/8
@ pj02
Though ur answer is correct, but i think the explaination is wrong.
Ur last line says "Now these 3 can be arranged in 3! Ways."
We are just asked to select people and not arrange.
Please correct me if I am wrong.
-Nipun Bansal
Please post OA.
I think order/arrangement here is not important, as the Probability of either of them(boy or gal) being born is same i.e 1/2
=> 1/2*1/2*1/2=1/8. Option A
Probability of having a boy out of 3 children is P(b) * P(g) * P(g) =1/2 * 1/2 * 1/2 = 1/8
bgg is 1/8
gbg is 1/8
ggb is 1/8
So overall: 3/8
pingu SaysVikram, I don't think order/arrangement is required here. Anyway lets us wait for the OA from PJ02
Probably the binomial expansion given below explains more clearly...initially even i was thinking that to be (1/
but after reading this, i learnt that even the order is important...
Of course, got this from somewhere else, but pasting here as it is useful..
Let X be the number of male children. X has the binomial distribution with n = 3 trials and success probability p = 0.5
In general, if X has the binomial distribution with n trials and a success probability of p then
P = n!/(x!(n-x)!) * p^x * (1-p)^(n-x)
for values of x = 0, 1, 2, ..., n
P = 0 for any other value of x.
The probability mass function is derived by looking at the number of combination of x objects chosen from n objects and then a total of x success and n - x failures.
Or, in other words, the binomial is the sum of n independent and identically distributed Bernoulli trials.
X ~ Binomial( n , p )
the mean of the binomial distribution is n * p = 1.5
the variance of the binomial distribution is n * p * (1 - p) = 0.75
the standard deviation is the square root of the variance = ( n * p * (1 - p)) = 0.8660254
The Probability Mass Function, PMF,
f(X) = P(X = x) is:
P( X = 0 ) = 0.125 all females
P( X = 1 ) = 0.375 one male, two females
P( X = 2 ) = 0.375 two males, one female
P( X = 3 ) = 0.125 three males
Answer has to be 3/8 ...arrangement does matter ...
Translate the same sum to coins ...If u flip 3 coins, what are the chances of getting exactly 1 head ?
Would the ans be 1/8 ? i could have head on the 1st, 2nd or 3rd flip ...and the other positions would automatically be tails ...so 3/8
Nipun, nothing wrong with pj02' s approach ....
Dividing total possiblilies by internal arrangements gives combinations .
Hence division of 3! has eliminated the arrangement element ...and it simply becomes selection i.e combination
simple one...
A credit card number has 6 digits (between 1 to 9). The first two digits are 12 in that order, the third digit is bigger than 6, the forth is divisible by 3 and the fifth digit is 3 times the sixth. How many different credit card numbers exist?a)27.b)36.c)72.d)112.e)422.
One more:
What is the probability of getting a sum of 8 or 14 when rolling 3 dice simultaneously?
a)1/6
b)
c)
d)21/216
e)32/216
I am back with Probability...
Two couples and one single person are seated at random in a row of five chairs. What is the probability that neither of the couples sits together in adjacent chairs?
A 1/5
B 2/5
C 3/5
D 4/5
E 3/8
Lengthy one:
There were ten friends four of whom are Sanjay, Salim, Reena and Teena. A team of six is to be formed such that Reena & Teena are never together but Sanjay and Salim are always together. How many teams can be made?
a.110
b.68
c.77
d.76
e.108
Solve it without using pen or paper..
Some of the people in Town X are left-handed, some are tall, some are both, and some are neither. InTown Y, three times as many people are left-handed as are left-handed in Town X, three times as many people are tall as are tall in Town X, three times as many people are both as are both in Town X, but no one is neither. If the total number of people in Town X is four times greater than the total number of people in Town Y, which of the following could be the number of people in Town X who are neither left-handed nor tall?
(A) 23
(B) 39
(C) 72
(D) 143
(E) 199
Solve it without using pen or paper..
Some of the people in Town X are left-handed, some are tall, some are both, and some are neither. InTown Y, three times as many people are left-handed as are left-handed in Town X, three times as many people are tall as are tall in Town X, three times as many people are both as are both in Town X, but no one is neither. If the total number of people in Town X is four times greater than the total number of people in Town Y, which of the following could be the number of people in Town X who are neither left-handed nor tall?
(A) 23
(B) 39
(C) 72
(D) 143
(E) 199
Solve it without using pen or paper..
Some of the people in Town X are left-handed, some are tall, some are both, and some are neither. InTown Y, three times as many people are left-handed as are left-handed in Town X, three times as many people are tall as are tall in Town X, three times as many people are both as are both in Town X, but no one is neither. If the total number of people in Town X is four times greater than the total number of people in Town Y, which of the following could be the number of people in Town X who are neither left-handed nor tall?
(A) 23
(B) 39
(C) 72
(D) 143
(E) 199
Try this one:
A Triangular field X is bordered by three square fields A, B and C whose areas are 144, 81 and 225 respectively. The area of the triangular field X is:
A) 150
B) 144
C) 80
D) 54
E) 36
Try this one:
A Triangular field X is bordered by three square fields A, B and C whose areas are 144, 81 and 225 respectively. The area of the triangular field X is:
A) 150
B) 144
C) 80
D) 54
E) 36
Three types of pencils, J,K, and L, cost $0.05, $0.10, and $0.25 each, respectively. If a box of 32 of these pencils costs a total of $3.40 and if there are twice as many K pencils as L pencils in the box, how many J pencils are in the box?
(A) 6
(B) 12
(C) 14
(D) 18
(E) 20
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Forty percent of the rats included in an experiment were male rats. If some of the rats died during the experiment and 30 percent of the rats that died were male rats, what was the ratio of the death rate among the male rats to the death rate among the female rats?
(A) 9/14
(B) 3/4
(C) 9/11
(D) 6/7
(E) 7/8
Three types of pencils, J,K, and L, cost $0.05, $0.10, and $0.25 each, respectively. If a box of 32 of these pencils costs a total of $3.40 and if there are twice as many K pencils as L pencils in the box, how many J pencils are in the box?
(A) 6
(B) 12
(C) 14
(D) 18
(E) 20
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Forty percent of the rats included in an experiment were male rats. If some of the rats died during the experiment and 30 percent of the rats that died were male rats, what was the ratio of the death rate among the male rats to the death rate among the female rats?
(A) 9/14
(B) 3/4
(C) 9/11
(D) 6/7
(E) 7/8
My take for the Rat problem is :
Total no .of Rats = 100 ===> M = 40 F = 60
Let no.of Dead = 50 === >M = 15 F = 35
So Death rate of M = 3/8 & F = 7/12
Final ratio === > 3/2 * 3/ 7 = 9/14
My ans for the below q is option c)14
no.of pencils = 32 of which one is twice the other.So J + 3L = 32. Only 2 options satisfy the above eqn.Trying with the cost only option c satisfies.
Three types of pencils, J,K, and L, cost $0.05, $0.10, and $0.25 each, respectively. If a box of 32 of these pencils costs a total of $3.40 and if there are twice as many K pencils as L pencils in the box, how many J pencils are in the box?
(A) 6
(B) 12
(C) 14
(D) 18
(E) 20