Examples(Set 1) - Probability

1. What is the probability of getting a number less than 4 when a die is rolled?
A. 1/ 2
B. 1/ 6
C. 1/ 3
D. 1/ 4

Answer: Option A

Explanation:
The possible outcomes when a die thrown is {1,2,3,4,5,6}.
Therefore, the number of possible outcomes of a die is 6.
i.e., n(S) = 6
Now, if we get a 4 on rolling die then the number of favourable outcome E = { 1 , 2 , 3 }
Hence, n(E) = 3
P(E) = n(E)/ n(S)
= 3/ 6
= 1/ 2






2.When tossing two coins once, what is the probability of tails on both the coins?
A. None of these
B. 1/ 4
C. 1/ 2
D. 3/ 4

Answer: Option B

Explanation:

total number of outcomes possible when two coins are tossed
S = {HH, HT, TH, TT}
n(S)=4
E = event of getting tails on both the coins = {TT}
n(E) = 1
P(E) = n(E)/ n(S)
= 1/ 4






3. Three coins are tossed. What is the probability of getting atleast two tails?
A. 1/ 2
B. 7/ 8
C. 1/ 8
D. 1/ 7

Answer: Option A

Explanation:
S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH}
n(S) = 8 E = event of getting atleast two Tails = {TTT, TTH, THT, HTT}
Hence, n(E) = 4
P(E) = n(E)/ n(S)
= 4/ 8
=1/2






4.A die is rolled twice. What is the probability of getting a sum equal to 8 ?
A. 2/ 3
B. 1/ 9
C. 1/ 6
D. 1/ 3

Answer: Option C

Explanation:
total number of outcomes possible when a die is rolled twice
n(S) = 6 × 6 = 36
E = Getting a sum of 8 when the two dice fall = { ( 2 , 6 ), ( 3 , 5 ) , ( 4 , 4 ) , ( 4 , 4 ) , ( 5 , 3 ), ( 6 , 2 ) }
Hence, n(E) = 6
P(E) = n(E)/ n(S)
= 6/ 36
= 1/ 6






5. A bag contains 2 yellow, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?
A. 10/ 21
B. 9/ 11
C. 1/ 2
D. 7/ 11

Answer: Option A

Explanation:
Total number of balls
= 2 + 3 + 2 = 7
Let S be the sample space.
n(S) = 7 C 2
n(E) = Number of ways of drawing 2 balls , none of them is blue = Number of ways of drawing 2 balls from the total 5
=5 C 2
P(E) = n(E)/ n(S)
= 5 C 2/ 7 C 2
= ( 5 × 4/ 2 × 1 )
   ( 7 × 6/ 2 × 1 )
= 10/ 21






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