Question

One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting

(i) a king of red colour.
(ii) a face card.
(iii)    a blackface card.
(iv)    a Jack of hearts.
(v) a spade
(vi)    a queen of diamond.

Solution

Total number of all possible outcomes = 52
i.e., n(S) = 52
(i) Let E be the favourable outcomes of getting a king of red colour, then n(E)= 2 Therefore,
P(E) = $fraction numerator straight n left parenthesis straight E right parenthesis over denominator straight n left parenthesis straight S right parenthesis end fraction equals 2 over 52 equals 1 over 26$

(it) Let F be the favourable outcomes of getting a face card, then
n(F) = 12
Therefore,
P(F) = $fraction numerator straight n left parenthesis straight F right parenthesis over denominator straight n left parenthesis straight S right parenthesis end fraction equals 12 over 52 equals 3 over 13$

(iii) Let G be the favourable outcomes of a red face card, then
n(G) = 6
P(G) = $fraction numerator straight n left parenthesis straight G right parenthesis over denominator straight n left parenthesis straight S right parenthesis end fraction equals 6 over 52 equals 3 over 26$

(iv) Let H be the favourable outcomes of getting a jack from the hearts, then n( H) = 1
Therefore,
P(H) = $fraction numerator straight n left parenthesis straight H right parenthesis over denominator straight n left parenthesis straight S right parenthesis end fraction equals 1 over 52$

(v) Let I be the favourable outcomes of getting a spade, then
n(I) = 13
Therefore:
P(l) = $fraction numerator straight n left parenthesis straight I right parenthesis over denominator straight n left parenthesis straight S right parenthesis end fraction equals 13 over 52 equals 1 fourth$

(vi) Let J be the favourable outcomes of getting a queen of diamonds, then n(J) = 1

Therefore,
P(J) = $fraction numerator straight n left parenthesis straight J right parenthesis over denominator straight n left parenthesis straight S right parenthesis end fraction equals 1 over 52.$

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Real Numbers

One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting

(i) a king of red colour.
(ii) a face card.
(iii)    a blackface card.
(iv)    a Jack of hearts.
(v) a spade
(vi)    a queen of diamond.

Some More Questions From Real Numbers Chapter

Probability of an event E + Probability of the event ‘not E’_______.

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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