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Real Numbers

Question
CBSEENMA10009381
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Five cards - the ten, jack, queen, king and ace of diamonds are well-shuffled with their face down wards. One card is then picked up at random.
(i)    What is the probability that the card is a queen?
(ii)    If the queen is drawn and put aside, what is the probability that the second card picked up is (a) an ace (b) a queen.

Solution

It is given that the total number of cards = 5
i.e.    n(S) = 5
(i) Let E be the favourable outcomes of getting a queen, then
E = {1}
⇒    n(E) = 1
Therefore,
P(E) = fraction numerator straight n left parenthesis straight E right parenthesis over denominator straight n left parenthesis straight S right parenthesis end fraction equals 1 fifth

(ii) If the Queen is drawn and put aside then possible outcomes become 4 i.e.,    n(S) = 4
(a) Let A be the favourable outcomes that the picked up card is an ace, then n(A) = {1}

Therefore,
P(A) = fraction numerator straight n left parenthesis straight A right parenthesis over denominator straight n left parenthesis straight S right parenthesis end fraction equals 1 fourth

(b) Let B be the favourable outcomes that the picked up card is a queen, then n(B) = 0

Therefore,
P(B) = fraction numerator straight n left parenthesis straight B right parenthesis over denominator straight n left parenthesis straight S right parenthesis end fraction equals 0 over 4 equals 0

Some More Questions From Real Numbers Chapter

The probability of an event that cannot happen is ________ Such an event is called __________.

The probability of an event that is certain to happen is ________ Such an event is called _________.

The sum of the probabilities of all the elemen-tary events of an experiment is ______.

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