In a family with 2 children there are four possibilities:
1) the first child is a boy and the second child is a boy (bb)
2) the first child is a boy and the second child is a girl (bg)
3) the first child is a girl and the second child is a boy (gb)
4) the first child is a girl and the second child is a girl (gg)
But already given that one child is boy. So we have three possibilities of (bb)(bg)(gb).
n(E)= both are boys=BB=1
n(S)= 3
Required probability P = n(E)/n(S) = 1/3.
The number of exhaustive outcomes is 36.
Let E be the event of getting an even number on one die and an odd number on the other. Let the event of getting either both even or both odd then = 18/36 = 1/2
P(E) = 1 - 1/2 = 1/2.
Number of ways of (selecting at least two couples among five people selected) = (?C? x ?C?)
As remaining person can be any one among three couples left.
Required probability = (?C? x ?C?)/¹?C?
= (10 x 6)/252 = 5/21
In a simultaneous throw of two dice, n(S) = 6 x 6 = 36
Let E = event of getting a doublet = { (1,1), (2,2), (3,3), (4,4), (5,5), (6,6)}
Total number of possible ways =
Number of favorable cases =
Therefore, required probability = 105/126 = 5/6
S = { (1, 1), (1, 2), (1, 3), (1, 4),(1, 5), (1, 6), (2, 1), (2, 2),.........(6, 5), (6, 6) }
=> n(S) = 6 x 6 = 36
E = {(6, 3), (5, 4), (4, 5), (3, 6) }
=> n(E) = 4
Therefore, P(E) = 4/36 = 1/9
Select a number which ocurs on two dice out of six numbers (1, 2, 3, 4, 5, 6). This can be done in , ways.
Now select two distinct number out of remaining 5 numbers which can be done in ways. Thus these 4 numbers can be arranged in 4!/2! ways.
So, the number of ways in which two dice show the same face and the remaining two show different faces is
=> n(E) = 720
n(S) = = 190
n(E) = = 105
Therefore, P(E) = 105/190 = 21/38
Vowels are A I A I O,
C A S T I G A T I O N
(O) (E) (O) (E) (O) (E) (O) (E) (O) (E) (O)
So there are 5 even places in which five vowels can be arranged and in rest of 6 places 6 constants can be arranged as follows :
Here, s={H,T} and E={H}
P(E) = n(E)/n(S) = 1/2
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