1.

Two cards are drawn, without replacement, from an ordinary pack of cards. Find the probability that at least one of the cards is red.1). 10/132). 15/4423). 10/174). 7/17

Answer»

Here, at least one of the two cards needs to be red.

This can be interpreted as: the required cases contain all the cases EXCEPT when NONE of the cards drawn is red.

We know that, there are 26 red and 26 black cards in a regular deck.

Let E3 be the event that none of the cards drawn is red, i.e. both the cards are black.

NUMBER of ways to draw 2 black cards out of 26 black cards = 26C2

PROBABILITY that none of the cards is red, P(E3) = 26C2/52C2 = 25/102

⇒ Probability that at least one is red = 1 – P(E3) = 1 – (25/102) = 77/102


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