Clearly, n(S) = 6 x 6 = 36
Let E be the event that the sum of the numbers on the two faces is divided by 4 or 6.
Then,E = {(1,3),(1,5),(2,2),(2,4),(2,6),(3,1),(3,3),(3,5),(4,2),(4,4),(5,1),(5,3),(6,2),(6,6)}
n(E) = 14.
Hence, P(E) = n(E)/n(S) = 14/36 = 7/18
Let S be the sample space.
Then, n(S) = number of ways of drawing 3 balls out of 15 = = = 455.
Let E = event of getting all the 3 red balls.
n(E) = = = 10.
=> P(E) = n(E)/n(S) = 10/455 = 2/91.
1 year = 365 days . A leap year has 366 days
A year has 52 weeks. Hence there will be 52 Sundays for sure.
52 weeks = 52 x 7 = 364days
366 ? 364 = 2 days
In a leap year there will be 52 Sundays and 2 days will be left.
These 2 days can be:
1. Sunday, Monday
2. Monday, Tuesday
3. Tuesday, Wednesday
4. Wednesday, Thursday
5. Thursday, Friday
6. Friday, Saturday
7. Saturday, Sunday
Of these total 7 outcomes, the favourable outcomes are 2.
Hence the probability of getting 53 days = 2/7
Clearly, n(S) = (6 x 6) = 36.
Let E = Event that the sum is a prime number.
Then E= { (1, 1), (1, 2), (1, 4), (1, 6), (2, 1), (2, 3), (2, 5), (3, 2), (3, 4), (4, 1), (4,3),(5, 2), (5, 6), (6, 1), (6, 5) }
n(E) = 15.
P(E) = n(E)/n(S) = 15/36 = 5/12.
Here, S = {1, 2, 3, 4, ...., 19, 20}.
Let E = event of getting a multiple of 3 or 5 = {3, 6 , 9, 12, 15, 18, 5, 10, 20}.
P(E) = n(E)/n(S) = 9/20.
Total number of outcomes possible, n(S) = 10 + 25 = 35
Total number of prizes, n(E) = 10
Here N and C are not common and same letters can be A, I, S, T. Therefore
Probability of choosing A = = 1/45
Probability of choosing I = = 1/45
Probability of choosing S = = 1/10
Probability of choosing T = = 1/15
Hence, Required probability =
Let A be the event of getting two oranges and
B be the event of getting two non-defective fruits.
and be the event of getting two non-defective oranges
=
Let S be the sample space.
Then, n(S) = =(52 x 51)/(2 x 1) = 1326.
Let E = event of getting 1 spade and 1 heart.
n(E)= number of ways of choosing 1 spade out of 13 and 1 heart out of 13 = = 169.
P(E) = n(E)/n(S) = 169/1326 = 13/102.
Let number of balls = (6 + 8) = 14.
Number of white balls = 8.
P (drawing a white ball) = 8 /14 = 4/7.
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