P(2 socks of matching colour) = P(drawing 2 blue socks) + P(drawing 2 red socks)

= P(Blue in first draw)*P(Blue in second draw) + P(Red in first draw)*P(Red in second draw)

= (2/4)*(1/3) + (2/4)*(1/3)

= (1/3)

Ans: B
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Total ways of choosing 2 out of 4 socks = 4C2 = 6

Favourable outcomes = both black or both red = 2

Favorable probability \(= \frac{2}{6} = \frac{1}{3}\)

Answer: Option B

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Solution

Given
In this question, we are given

A bag with two blue and two red socks
Two socks are randomly drawn out

To find
We need to determine

The probability that these two have the same color

Approach and Working out

Probability(same color) = Prob(both blue or both red)

Prob(both blue) = Prob(first blue, second blue) = \(\frac{2}{4}\) × \(\frac{1}{3}\) = \(\frac{1}{6}\)
Prob(both red) = Prob(first red, second red) = \(\frac{2}{4}\) × \(\frac{1}{3}\) = \(\frac{1}{6}\)

Prob(both blue or both red) = \(\frac{1}{6}\) + \(\frac{1}{6}\) = \(\frac{2}{6}\) = \(\frac{1}{3}\)

Thus, option B is the correct answer.

Correct Answer: Option B
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No matter easy or tough, probability questions are always fun to solve

1. We have 2 red and 2 blue socks and a total of 4 socks

2. What is the probability that that they are matching in color? - In other words, what is the probability of picking 2 red socks or 2 blue socks in a row

3. Probability of picking 2 blue socks is \(= \frac{2}{4} * \frac{1}{3} = \frac{1}{6}\)

4. OR Probability of picking 2 red socks is \(= \frac{2}{4} * \frac{1}{3} = \frac{1}{6}\)

5. Adding 3. and 4. we get, \(\frac{1}{6} + \frac{1}{6} = \frac{2}{6} = \frac{1}{3}\)

Ans. B
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Solution:

P(matching color socks) = P(blue followed by blue) + P(red followed by red)

= 2/4 * 1/3 + 2/4 * 1/3

= 1/6 + 1/6 = 1/3

Answer: B
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