Question

19. Hassan keeps picking playing cards out of a standard deck of 52 cards, hoping that he will (1 point) draw a queen. There are four queens in the deck. After looking at each card, he places it back in the deck. What is the probability that Hassan will draw a queen in the first seven attempts? 043% 046% 57% 68%

Answer 1

The probability of getting a queen in a randomly selected draw

$= \frac{4}{52} = \frac{1}{13}$

Let X denotes the number of queen drawn in the first seven attempts.

X ~ Binomial(n = 7, p = 1/13)

The probability mass function of X is

$P(X=x) = \binom{7}{x}*(\frac{1}{13})^x*(1 - \frac{1}{13})^{7-x},x=0,1,2,3,..,7$

The probability that Hassan will draw a queen in the first seven attempts

$= P(X \geq 1)$

$=1 - P(X = 0)$

$= 1 - (1 - \frac{1}{13})^{7 - 0}$

$= 1 - 0.571038$

$= 0.428962$

$\approx 0.43$

$\approx 43\%$