Question

Four cards bearing the numbers 2, 3, 4 and 5 are placed on the table. Two cards are selected from these four cards to form a two-digit number. List the sample space. Find the probability that the number formed

a) Is divisible by 3.

b) Is greater than 33

c) Is a multiple of 11

d) Is less than 55.

Answer 1

Note: Final answers are highlighted in colour.

Sample space= {23,24,25,32,34,35,42,43,45,52,53,54}

Count of possible outcomes(N)= 12

a) Probability that the number is divisible by 3

Outcomes that are supporting the case={24,42,45,54}

n(favourable outcomes)=4

Proabability= n(favourable outcomes)/ N= 4/12= 1/3

b)Probability that the number is greater than 33.

Outcomes that are supporting the case={34,35,42,43,45,52,53,54}

n(favourable outcomes)=8

Proabability= n(favourable outcomes)/ N= 8/12= 2/3

c)Probability that the number is a multiple of 11

Outcomes that are supporting the case={}

n(favourable outcomes)=0

Proabability= n(favourable outcomes)/ N= 0/12= 0

This is called an impossible event

d)Probability that the number is less than 55

Outcomes that are supporting the case={23,24,25,32,34,35,42,43,45,52,53,54}

n(favourable outcomes)=12

Proabability= n(favourable outcomes)/ N= 12/12= 1

Probability of 1 means it is a certain event. Selection of any 2 cards satisfies the given condition.