Maths Questions

1. Eleven cards are each marked with one letter so that together they make up the word 'MATHEMATICS'. If 3 cards are drawn at random, find the probability that they can make up the word 'CAT'.

There are altogether 11 cards, 1 card of "C", 2 cards of "A" and 2 cards of "T".

Total number of combination that can be drawn = 11C3 = 165
The number of CAT that can be srawn = 1 x 2 x 2 = 4
Therefore probability = 4/165

2. The probabilities that Thomas and Jerry will attend a meeting are 0.6 and 0.7 respectively. What is the probability that at least one of them attends the meeting?

The probability that at least one of them attends = 1 - probability that both do not attend.

Probability of Thomas will not attend = 1 - 0.6 = 0.4
Probability of Jerry will not attenf = 1- 0.7 = 0.3
The probability that at least one of them attends = 1 - (0.4)(0.3) = 0.88

3. Three marksmen take part in a shooting contest and their probabilites of hitting the target are 1/3, 1/4 and1/5. Find the probability that the target is hit if they fire simultaneously.

The probability that they all miss is (1-1/3)(1-1/4)(1-1/5)
=(2/3)(3/4)(4/5) = 2/5
The probability of at least of them hit the target = 1 - 2/5 = 3/5