**Probability- Key Points**

**Probability- Key
Points-aptitude-questions-answers-basics**

**Probability
Aptitude basics, practice questions, answers and explanations **

**Prepare for companies tests and interviews**

Probability of an event= (No of
occurrences of an event)/(Total no. of possible outcomes)

P(E) = n(E)/n(U)

where n(E)= no. of occurrences of event; n(U)= total possible outcomes

Probability of head in a toss=1/2

Probability of tails in a toss=1/2

Probability of any side in a throw of dice=1/6

Probability of getting a sign in a deck of cards= 1/4

Probability of getting an ace; king; queen etc= 1/13

Probability of occurrence of 2 independent events= P(A)*P(B)

**Exercise Questions**

1. If 10 letters are to be placed in 10
addressed envelopes, then what is the probability that at least one letter is
placed in wrong addressed envelope?

a.1/10!

b.1/9!

c.1- (1/10!)

d.9/10

2.Two letters are selected randomly from
English alphabet simultaneously. What is the probability that one is a constant
and the other a vowel?

a.10/67

b.21/65

c.44/65

d.2/13

3. Two dice are rolled together. The
probability that the sum of the numbers shown on the two dice is maximum or
minimum is??

a.1/18

b.1/9

c.1/6

d.1/36

4. A bag has 5 red balls and 3 green
balls and another bag contains 4 green balls and 3 red balls. If one ball is
drawn from each bag, then what is the probability that both are green balls?

a.5/14

b.3/14

c.11/14

d.9/14

5. Two cards are drawn at random from a
pack of cards. The probability that both are queens or diamonds is??

a.20/221

b.15/221

c.13/221

d.14/221

6. If a coin is tossed 6 times, then the
probability of getting exactly 1 head is ???..

a.1/32

b.13/32

c.5/32

d.3/32

7. Amit throws a biased coin on which
the head appears in 65% of the situations. In a game involving this coin, if
Amit is paid Rs.15 per head and he has to pay Rs.20 for a tail, then in the
long run, per game Amit makes an average??

a.Profit of Rs.2.25

b.loss of Rs.2.25

c.profit of Rs.2.75

d.loss of Rs.2.75

8. From a box containing a dozen bulbs,
of which exactly one half are good, and four bulbs are chosen at random to fit
into the four bulb holders in a room. The probability that the room gets
lighted is????

a.2/3

b.1/3

c.33/44

d. 32/33

9. From a bag containing 6 pink and 8
orange balls, 8 balls are drawn at random. The probability that 5 of them are
pink and the rest are orange is????

a.16/143

b.19/143

c.17/143

d. 13/143

10. A bag contains 5 five-rupee coins, 8
two-rupee coins and 7 one-rupee coins. If four coins are drawn from the bag at
random, then find the odds in favour of the draw yielding the maximum possible
amount.

a.1:968

b.968:969

c.1:969

d.969:968

**Answer Key**

1.c; 2.b; 3.a; 4.b; 5.d; 6.d; 7.c; 8.d;
9.a; 10.a