Question

In a lottery, there are 10 prizes and 25 are empty. Find the probability of getting a prize. Also verify that. P(E)+ P(not E) =1 for this event .

Answer 1

The probability of happening of an event always lies 0 to 1 and in percentage it lies 0 % to 100 % .
The sum of all the probabilities of all possible outcomes of experiment is 1.
P(Event) + P (not an Event) = 1.

Probability of an event can never be negative.

SOLUTION:

Given:
Number of prizes in a lottery= 10
Number of empty prizes in a lottery= 25

Total number of lotteries= 35
Total number of outcomes= 35
Number of favourable outcomes= 10

Probability = Number of favourable outcomes / Total number of outcomes.

Required probability= P(getting a prize)= 10/35= 2/7

P(Event)prize = 2/7
P(not Event)=25/35= 5/7

P(Event) + P (not an Event) = 1

2/7 + 5/7 = 1
(2+5)/7 = 1
7/7 = 1

1 = 1

Hence, P(Event) + P (not an Event) = 1 is verified.

HOPE THIS WILL HELP YOU...

Answer 2

Total no..of outcome = 10+25 =35
probability of getting prize = no..of favourable event /total outcome
=10/35.
Verify
P not E = 25/35
so pE+ pE not =25/35 +10/35 =35/35 or 1..
Hope u understand