Elementary Probability Problems

Introduction :

The measure of how possible it is that a number of event will occur; a number expressing the ratio of favorable cases to the whole number of cases possible  the quality of being probable; a probable event or the most probable event; "for a while mutiny seemed a probability"; "going by past experience there was a high probability that the visitors were lost"


Problems of Elementary Probability


Example:

At a car park there are 100 vehicles, 60 of which are cars, 30 are vans and the remainder are Lorries. If every vehicle is equally possible to depart, find the probability of:

a) Van leaving first.

b) Lorry leaving first.

c) Car leave-taking second if either a lorry or van had left first.

Solution:

a) Let S be the sample space and A be the event of a van leaving first.

n(S) = 100

n(A) = 30

Probability of a van leaving first:

P(A) = 30 / 100

P(A) = 3 / 10

b) Let B be the event of a lorry leaving first.

N(B) = 100 – 60 – 30 = 10

Probability of a lorry leaving first:

P(B) = 10 / 100

P(B)= 1 / 10

c) If either a lorry or van had left first, then there would be 99 vehicles remaining, 60 of which are cars. Let T be the sample space and C be the event of a car leaving.

n(T) = 99

n(C) = 60

Probability of a car leave-taking behind a lorry or van has left:

P(C) = 60 / 99

= 20 / 33

P ( C ) =  20 / 33

2. A die is roll, find the probability that an even number is obtain.

Solution:

Let us 1st write the sample space S of the experimentation.

S = {1,2,3,4,5,6}

Let E be the event "an even number is obtain" and write it down.

E = {2,4,6}

We now use the formula of the standard probability.

P(E) = n(E) / n(S)

= 3 / 6

= 1 / 2

Answer : P(E) = 1 / 2

3 . 2 coins are tossed, find the probability that 2 heads are obtained.

Solution :

The sample space S is given by.

S = {(H,T), (H,H), (T,H), (T,T)}

Let E be the event "two heads are obtained".

E = {(H,H)}

We use the formula of the standard probability.

P(E) = n(E) / n(S)

= 1 / 4

Answer : P(E) = 1 / 4