Question Detail
In a throw of coin what is the probability of getting tails.
- 1
- 2
- 1/2
- 0
Answer: Option C
Explanation:
Total cases = [H,T] - 2
Favourable cases = [T] -1
So probability of getting tails = 1/2
1. Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even ?
- 3/4
- 1/4
- 7/4
- 1/2
Answer: Option A
Explanation:
Total number of cases = 6*6 = 36
Favourable cases = [(1,2),(1,4),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(3,2),(3,4),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,2),(5,4),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)] = 27
So Probability = 27/36 = 3/4
2. Three unbiased coins are tossed, what is the probability of getting at least 2 tails ?
- 1/3
- 1/6
- 1/2
- 1/8
Answer: Option C
Explanation:
Total cases are = 2*2*2 = 8, which are as follows
[TTT, HHH, TTH, THT, HTT, THH, HTH, HHT]
Favoured cases are = [TTH, THT, HTT, TTT] = 4
So required probability = 4/8 = 1/2
3. A box contains 5 green, 4 yellow and 3 white balls. Three balls are drawn at random. What is the probability that they are not of same colour.
- 52/55
- 3/55
- 41/44
- 3/44
Answer: Option C
Explanation:
\begin{aligned}
\text{Total cases =} ^{12}C_3 \\
= \frac{12*11*10}{3*2*1} = 220 \\
\text{Total cases of drawing same colour =} \\
^{5}C_3 + ^{4}C_3 + ^{3}C_3 \\
\frac{5*4}{2*1} + 4 + 1 = 15 \\
\text{Probability of same colur =} = \frac{15}{220}\\
= \frac{3}{44} \\
\text{Probability of not same colur =} \\
1-\frac{3}{44}\\ = \frac{41}{44}
\end{aligned}
4. What is the probability of getting a sum 9 from two throws of dice.
- 1/3
- 1/9
- 1/12
- 2/9
Answer: Option B
Explanation:
Total number of cases = 6*6 = 36
Favoured cases = [(3,6), (4,5), (6,3), (5,4)] = 4
So probability = 4/36 = 1/9
5. A speaks truth in 75% of cases and B in 80% of cases. In what percentage of cases are they likely to contradict each other, narrating the same incident
- 30%
- 35%
- 40%
- 45%
Answer: Option B
Explanation:
Let A = Event that A speaks the truth
B = Event that B speaks the truth
Then P(A) = 75/100 = 3/4
P(B) = 80/100 = 4/5
P(A-lie) = 1-3/4 = 1/4
P(B-lie) = 1-4/5 = 1/5
Now
A and B contradict each other =
[A lies and B true] or [B true and B lies]
= P(A).P(B-lie) + P(A-lie).P(B)
[Please note that we are adding at the place of OR]
= (3/5*1/5) + (1/4*4/5) = 7/20
= (7/20 * 100) % = 35%