Probability Questions Answers

8. In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither blue nor green?
 2/3
 8/21
 3/7
 9/22
Answer And Explanation
Answer: Option B
Explanation:
Total number of balls = (8 + 7 + 6) = 21
Let E = event that the ball drawn is neither blue nor green =e vent that the ball drawn is red.
Therefore, n(E) = 8.
P(E) = 8/21. 
9. A card is drawn from a pack of 52 cards. The probability of getting a queen of club or a king of heart is
 1/13
 2/13
 1/26
 1/52
Answer And Explanation
Answer: Option C
Explanation:
Total number of cases = 52
Favourable cases = 2
Probability = 2/56 = 1/26 
10. From a pack of 52 cards, 1 card is drawn at random. Find the probability of a face card drawn.
 3/13
 1/52
 1/4
 None of above
Answer And Explanation
Answer: Option A
Explanation:
Total number of cases = 52
Total face cards = 12 [favourable cases]
So probability = 12 /52 = 3/13 
11. A box contains 20 electric bulbs, out of which 4 are defective. Two bulbs are chosen at random from this box. The probability that at least one of these is defective is
 \begin{aligned} \frac{7}{19} \end{aligned}
 \begin{aligned} \frac{6}{19} \end{aligned}
 \begin{aligned} \frac{5}{19} \end{aligned}
 \begin{aligned} \frac{4}{19} \end{aligned}
Answer And Explanation
Answer: Option A
Explanation:
Please remember that Maximum portability is 1.
So we can get total probability of non defective bulbs and subtract it form 1 to get total probability of defective bulbs.
So here we go,
Total cases of non defective bulbs
\begin{aligned}
^{16}C_2 = \frac{16*15}{2*1} = 120 \\
\text{total cases = } \\
^{20}C_2 = \frac{20*19}{2*1} = 190 \\
\text{probability = } \frac{120}{190} = \frac{12}{19} \\
\text{P of at least one defective = } 1 \frac{12}{19} \\
=\frac{7}{19}
\end{aligned} 
12. 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 And Explanation
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(Alie) = 13/4 = 1/4
P(Blie) = 14/5 = 1/5
Now
A and B contradict each other =
[A lies and B true] or [B true and B lies]
= P(A).P(Blie) + P(Alie).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%

13. From a pack of 52 cards, two cards are drawn together, what is the probability that both the cards are kings
 2/121
 2/221
 1/221
 1/13
Answer And Explanation
Answer: Option C
Explanation:
\begin{aligned}
\text{Total cases =} ^{52}C_2 \\
= \frac{52*51}{2*1} = 1326 \\
\text{Total King cases =} ^{4}C_2 \\
= \frac{4*3}{2*1} = 6 \\
\text{Probability =} = \frac{6}{1326}\\
= \frac{1}{221} \\
\end{aligned} 
14. 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 And Explanation
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}