A box contains identical cards on each card a letter of the English alphabet is printed.A card is selected at random from the box and not replaced and a second card is then selected. Find the probability that two cards selected (II) the other consonant?

Answer 1

Consonant Probability Calculation

There are 26 letters in the English alphabet, of which 21 are consonants (B, C, D, F, G, H, J, K, L, M, N, P, Q, R, S, T, V, W, X, Y, Z) and 5 are vowels (A, E, I, O, U).

The probability of selecting a consonant on the first draw is 21/26, since there are 21 consonants out of 26 total cards.

After the first card is drawn and not replaced, there are now 25 cards remaining in the box, of which 20 are consonants and 5 are vowels.

Therefore, the probability of selecting a consonant on the second draw, given that the first card was a consonant and was not replaced, is 20/25 or 4/5.

Using the multiplication rule of probability, we can multiply the probabilities of the two events happening sequentially to get the probability of both events happening together:

P(both cards are consonants) = P(first card is a consonant) * P(second card is a consonant given that the first card was a consonant and was not replaced) = (21/26) * (20/25) = 0.64 or 64%

Therefore, the probability that both cards selected are consonants is 0.64 or 64%.

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