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.
Total number of elementary events =
Number of ways of selecting exactly one defective bulb out of 3 and 4 non-defective out of 7 is
So,required probability = / = 5/12.
P(atleast B) = P( B or A) = P(B) + P(A) = (0.3) + (0.4) = 0.7
One person can select one house out of 3= ways =3.
Hence, three persons can select one house out of 3 in 3 x 3 x 3 =9.
Therefore, probability that all thre apply for the same house is 1/9
3 letters can be choosen out of 9 letters in ways.
More than one vowels ( 2 vowels + 1 consonant or 3 vowels ) can be choosen in ways
Hence,required probability = = 17/42
We know that,
Total number of balls n(S) = 26
Number of vowels n(E) = 5
Hence, required probability = n(E)/n(S) = 5/26.
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.
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 =
=
= =
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.
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 = =
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.
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