Maths Questions

1. There are 4 identical pairs of red gloves and 2 identical pairs of black gloves in a drawer. Miss Fong picks two gloves at random. What is the probability that a left-hand glove and a right- hand glove of the same colour are picked?

Use RL, RR, BL and BR represents colour-hand combination where first R=Red, first B=Black, second R=Right and second L = Left.

The number of gloves are respectively 4, 4, 2 and 2 of total 12.

Number of combinations for the 2 gloves = 12C2 = 66

Number of combinations for RL + RR = 4x4 =16
Number of combinations for BL + BR = 2x2 = 4

The required probability = (16+4)/66 = 10/33

2. A test consists of 4 multiple choice questions. Each question has 5 optons. A student will pass his test f he gets at least 3 of them correct.

If John attempts the questions by guesting, find the probability that he can pass the test.

The number of guesses he can make for one question is 5.
The probability that he will guess right for a question = 1/5
The probability that he will guess wrong for a question = 4/5

Probability of guessing right 3 questions = 4C3 x (1/5)(1/5)(1/5)(4/5)
=16/625
Probability of guessing right 4 questions = 4C4 x (1/5)(1/5)(1/5)(1/5)
=1/625

Probability of passing the test = (16+1)/625 = 17/625

3. Two cards are drawn at random from ten cards marked from 1 to 10. What is the probability that the sum of th numbers shown on the cards drawn is 12?

Number of combinations for drawing two cards = 10C2 = 45
Combinations to get 12 are: 3+9; 4+8; 5+7; 6+6 total 4 cases
Therefore the requires probability = 4/45

(3)

Combinations to get 12 should be: 2+10;3+9; 4+8; 5+7 total 4 cases