If two fair dice are tossed, then what is the probability that the sum of the numbers on the faces of the dice is neither 5 nor 7?
\(\dfrac{13}{18}\)
Out of 36 equally likely outcomes, the sum equals 5 in 4 ways \(\{(1,4),(2,3),(3,2),(4,1)\}\) and equals 7 in 6 ways \(\{(1,6),(2,5),(3,4),(4,3),(5,2),(6,1)\}\). So \(P(5\text{ or }7) = \dfrac{10}{36} = \dfrac{5}{18}\), and the required probability is \(1-\dfrac{5}{18} = \dfrac{13}{18}\).
Similar Questions
Let A, B and C be three mutually exclusive and exhaustive events associated with a random experiment. If P (B) = 1.5 P (A) and P (C) = 0.5 P (B), then P (A) is equal to
A point is chosen at random inside a rectangle measuring 6 inches by 5 inches. What is the probability that the randomly selected point is at least one inch from the edge of the rectangle?
In throwing of two dice, the number of exhaustive events that ‘5’ will never appear on any one of the dice is
Two independent events A and B have \({\rm{P}}\left( {\rm{A}} \right) = \frac{1}{3}\) and \({\rm{P}}\left( {\rm{B}} \right) = \frac{3}{4}\) . What is the probability that exactly one of the two events A or B occurs?
A problem in statistics is given to three students A, B and C whose chances of solving it independently are \(\frac{1}{2},\frac{1}{3}\) and \(\frac{1}{4}\) respectively. The probability that the problem will be solved is
The probabilities that a student will solve Question A and Question B are 0.4 and 0.5 respectively. What is the probability that he solves at least one of the two questions?
If a coin is tossed till the first head appears, then what will be the sample space?
A committee of three has to be chosen form a group of 4 men and 5 women. If the selection is made at random, what is the probability that exactly two members are men?
A pair of fair dice is rolled. What is the probability that the second dice lands on a higher value than does the first?
What is the probability of getting a composite number in the list of natural numbers from 1 to 50?
Important Questions from Probability of Random Experiments
Let A, B and C be three mutually exclusive and exhaustive events associated with a random experiment. If P (B) = 1.5 P (A) and P (C) = 0.5 P (B), then P (A) is equal to
Five persons A, B, C, D and E occupy seats in a row at random. The probability that A and B sit next to each other is:
The probability of getting 9 cards of the same suit in one hand at a game of bridge is:
If the probability of A to fail in an examination is 0.2 and that for B is 0.3, then, the probability that either A or B fails is:
A problem in Mathematics is given to 3 students A, B and C. If the probability of A solving the problem is \(\dfrac{1}{2}\) and B not solving it is \(\dfrac{1}{4}\) and the whole probability of the problem being solved is \(\dfrac{63}{64}\), then what is the probability of solving it by C?
