Question

what is the probability that atleast 1 out of seven cards will be drawn from a standard deck of playing card will be a jack

Answer 1

solution:

From the given information

Total no.of cards in a deck = 52

No.of jacks = 4

No.of remaining cards = 52 - 4 = 48

When you draw a 7 cards from a deck of cards

Total no.of possible outcomes = n(S) = 52C7 = 133784560

Let A be the event that atleast 1 card out of 7 cards drawn is a jack

Then A' is the event represents none of them are jacks when 7 cards are drawn

n(A') = 48C7 = 73629072

Probability that atleast 1 out of 7 cards drawn will be a jack = P(A)

= 1 - P(A')

= 1 - n(A') / n(S)

= 1 - 73629072 / 133784560

= 1 - 0.5504

=~ 0.4496

Probability that atleast 1 out of 7 cards drawn will be a jack = 0.4496