Probability giving Problems

Probability Level 2

If two small squares of selected at random from a chess board then the probability that they have exactly one common vertex is

\dfrac{1}{72}

\dfrac{7}{72}

\dfrac{1}{144}

\dfrac{7}{144}

1 solution

Pulkit Gupta
Jan 27, 2016

If the squares are to share a common vertex ( or corner) they must lie on two adjacent columns. You will find there are SEVEN such adjacent columns for us to pick.

Let us randomly pick a pair of out of the seven possible & find the number of favorable squares for it.

For squares lying at the topmost and bottom most positions, there is only one such square for it to pair up i.e. 2 * 1=2 favorable cases.

For the other 6 squares lying in the chosen column, there are two possible squares for it to pair up i.e. 6 * 2=12 favorable cases.

Thus we find the total favorable cases for a chosen adjacent pair of columns as (2+12)=14.

Multiplying 14 by 7 (=98) gives us the total favorable cases.

Sample space is the number of ways of choosing 2 squares out of 64 i.e. 64 choose 2 =2016 ways.

Probability is thus, $\large \frac{98}{2016} = \frac{7}{144}$

I didn't got ur method

Aman Dubey - 5 years, 4 months ago

Which part?

Try to visualize what I have written. This may help.

Pulkit Gupta - 5 years, 4 months ago

As you have written in 3rd paragraph there is only two such topmost and bottom most positions ie at the corners so then how can u multiply this by 7

Aman Dubey - 5 years, 4 months ago

Probability giving Problems

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