Question

If the probability of an event P(E) then = a/b then ______.

(A) a > b
(B) a < b
(C) a ≥ b
(D) a ≤ b

No Irrevelent answers​

Answer 1

Answer:

D is the answer of this probability

Answer 2

Answer:

If the probability of an event P ( E ) is a / b, then a ≤ b.

Option D) a ≤ b

Step-by-step-explanation:

We have given that,

The probability of an event P ( E ) is a / b.

We have to find the relation between a and b.

We know that,

Probability of an event [ P ( A ) ] = [ n ( A ) / n ( S ) ]

Where, A is an event and S is the sample space.

Here,

P ( E ) = a / b

∴ The number of outcomes of the event is a.

And the number of sample spaces is b.

Let the event E be an even number which is divisor of 30.

∴ S = { 1, 2, 3, 5, 6, 10, 15, 30 }

n ( S ) = b = 8

E = { 2, 6, 10, 30 }

n ( E ) = a = 4

∴ P ( E ) = [ n ( E ) / n ( S ) ]

⇒ P ( E ) = a / b

⇒ P ( E ) = 4 / 8

⇒ P ( E ) = 1 / 2

⇒ P ( E ) = 0.5

From this, we conclude that,

The number of outcomes of an event "E" i. e. "a" is 4.

And the number of sample spaces i. e. "b" is 8.

∴ a = 4 < b = 8

⇒ a < b

Also,

P ( E ) = 0.5

This indicates that the probability of an event is always either greater than or equal to "0" or less than or equal to "1".

∴ For the probability of an event to be equal to zero, "a" should be always equal to zero.

∴ a < b - - - ( 1 )

And for the probability of an event to be equal to one, "a" should be always equal to "b".

∴ a = b - - - ( 2 )

From ( 1 ) & ( 2 ), we can conclude that,

The number of outcomes of an event should be always either less than or equal to the number of sample spaces.

∴ a ≤ b

∴ If the probability of an event P ( E ) is a / b, then a ≤ b.