Probability Questions and Answers

Q: In a drawer there are 4 white socks, 3 blue socks and 5 grey socks. Two socks are picked randomly. What is the possibility that both the socks are of same color?

There are \( 4 + 3 + 5 = 12 \) socks in all.\[ \text{total ways} = {}^{12}C_{2} = 66 \]Same colour, counted by colour:\[ {}^{4}C_{2} + {}^{3}C_{2} + {}^{5}C_{2} = 6 + 3 + 10 = 19 \]\[ P = \frac{19}{66} \]The three colours are mutually exclusive, so their counts simply add.

Q: A bag contains 6 black and 8 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?

The bag holds \( 6 + 8 = 14 \) balls.\[ P = \frac{8}{14} = \frac{4}{7} \]The denominator is the total, not the number of black balls - using 6 would give \( \tfrac{4}{3} \), which is not even a valid probability.

Q: If a number is chosen at random from the set {1, 2, 3, ...., 100}, then the probability that the chosen number is a perfect cube is -.

The perfect cubes up to 100 are\[ 1^{3} = 1,\quad 2^{3} = 8,\quad 3^{3} = 27,\quad 4^{3} = 64 \]since \( 5^{3} = 125 \) is already too large.\[ P = \frac{4}{100} = \frac{1}{25} \]

Important Instructions

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In a drawer there are 4 white socks, 3 blue socks and 5 grey socks. Two socks are picked randomly. What is the possibility that both the socks are of same color?