Probability problems
- 1. Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even?
Options- A. 3/4
- B. 3/8
- C. 5/16
- D. 2/7 Discuss
Correct Answer: 3/4
Explanation:
In a simultaneous throw of two dice, we have n(S) = (6 x 6) = 36.
Then, E= {(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)}
n(E) = 27.
P(E) = n(E)/n(S) = 27/36 = 3/4.
- 2. What is the probability of getting a sum 9 from two throws of a dice?
Options- A. 1/2
- B. 3/4
- C. 1/9
- D. 2/9 Discuss
Correct Answer: 1/9
Explanation:
In two throws of a die, n(S) = (6 x 6) = 36.
Let E = event of getting a sum ={(3, 6), (4, 5), (5, 4), (6, 3)}.
P(E) =n(E)/n(S)=4/36=1/9.
- 3. In a single throw of two dice , find the probability that neither a doublet nor a total of 8 will appear.
Options- A. 7/15
- B. 5/18
- C. 13/18
- D. 3/16 Discuss
Correct Answer: 5/18
Explanation:
n(S) = 36
A = {(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)}
B = { (2, 6), (3, 5), (4, 4), (5, 3), (6, 2) }
Required probability =
=
= =
- 4. 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 red nor green?
Options- A. 1/3
- B. 3/5
- C. 8/21
- D. 7/21 Discuss
Correct Answer: 1/3
Explanation:
Total number of balls = (8 + 7 + 6) = 21.
Let E = event that the ball drawn is neither red nor green
= event that the ball drawn is blue.
n(E) = 7.
P(E) = n(E)/n(S) = 7/21 = 1/3.
- 5. Four dice are thrown simultaneously. Find the probability that all of them show the same face.
Options- A. 1/216
- B. 1/36
- C. 2/216
- D. 4/216 Discuss
Correct Answer: 1/216
Explanation:
The total number of elementary events associated to the random experiments of throwing four dice simultaneously is:
=
n(S) =
Let X be the event that all dice show the same face.
X = { (1,1,1,1,), (2,2,2,2), (3,3,3,3), (4,4,4,4), (5,5,5,5), (6,6,6,6)}
n(X) = 6
Hence required probability = =
- 6. The probability that z lies between 0 and 3.01
Options- A. 0.4987
- B. 0.5
- C. 0.9987
- D. 0.1217 Also asked in: AIEEE, Bank Exams, CAT, Analyst, Bank Clerk, Bank PO
Correct Answer: 0.4987
Explanation:
Probability between z = 0 and z = 3.01 is given by
P(0<z<3.01) = P(z<3.01) - P(z<0)
Reading from the z-table, we have
P(z<0) = 0.5
P(z<3.01) = 0.9987
Hence, P(0<z<3.01) = 0.9987 - 0.5 = 0.4987.
- 7. What is the probability that a number is divisible by 4?
Options- A. 2
- B. 1/2
- C. 1/4
- D. 1 Also asked in: AIEEE, Bank Exams, CAT, Analyst, Bank Clerk, Bank PO
Correct Answer: 1/2
Explanation:
Probability is Number of favourable outcomes by total outcomes
Total comes = 2 (Divisible or not)
Favourable = 1 (Divisible)
Hence, probability = 1/2.
- 8. Two dice are rolled simultaneously. Find the probability of getting the sum of numbers on the on the two faces divisible by 3 or 4?
Options- A. 3/7
- B. 7/11
- C. 5/9
- D. 6/13 Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: 5/9
Explanation:
Here n(S) = 6 x 6 = 36
E={(1,2),(1,5),(2,1),(2,4),(3,3),(3,6),(4,2),(4,5),(5,1),(5,4),(6,3) ,(6,6),(1,3),(2,2),(2,6),(3,1),(3,5), (4,4),(5,3),(6,2)}
=> n(E)=20
Required Probability n(P) = n(E)/n(S) = 20/36 = 5/9.
- 9. In a simultaneous throw of pair of dice. Find the probability of getting the total more than 7.
Options- A. 1/2
- B. 5/12
- C. 7/15
- D. 3/12 Discuss
Correct Answer: 5/12
Explanation:
Here n(S) = (6 x 6) = 36
Let E = event of getting a total more than 7
= {(2,6),(3,5),(3,6),(4,4),(4,5),(4,6),(5,3),(5,4),(5,5),(5,6),(6,2),(6,3),(6,4),(6,5),(6,6)}
Therefore,P(E) = n(E)/n(S) = 15/36 = 5/12.
- 10. A number X is chosen at random from the numbers -3, -2, -1, 0, 1, 2, 3. What is the probability that |X|<2
Options- A. 3/7
- B. 3/4
- C. 4/5
- D. 5/7 Discuss
Correct Answer: 3/7
Explanation:
X can take 7 values.
To get |X|+2) take X={?1,0,1}
=> P(|X|<2) = Favourable CasesTotal Cases = 3/7
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