Probability Practice Test 1

Question : 10 of 40

Marks: +1, -0

Six playing cards are lying face down on a table, where two of them are kings. Two cards are drawn at random. Let a denote the probability that at least one or the cards drawn is king, and b denote the probability of not drawing a king. The ratio

a/b

is:

≥ 0.25 and < 0.5
≥ 0.5 and < 0.75
≥ 0.75 and < 1.0
≥ 1.0 and < 1.25
≥ 1.25

Validate

Solution:

There are three scenarios.
Either two are kings, only one card is king, none of the two is king.
In all, the number of combinations of taking 2 cards out of 6

= ^6C_2 =6!/{4!×2!}=15

Split of this is like this:
The number of combinations of the two cards being kings =

^2C_2 = 1

The number of combinations of only one card being a king

= ^2C_1 × ^4C_1 = 2 × 4 = 8

The number of combinations of neither cards being a king

=^4C_2 = 6

Now, a = P(at least one king) = P(one king) + P(two king)

=(8+1)1/15=3/5

b = P(no king)

=6/15=2/5

⇒a/b=3/2=1.5

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