Question

A card is drawn from a deck of cards numbered one through twenty. The card is NOT replaced and another card is drawn. Find the probability of the outcome.
P(two prime numbers are drawn in a row)

A) 16/95
B) 14/95
C) 4/25
D) 5/13

Answer 1

Answer:

B)  P(two prime numbers are drawn in a row) = 14/95

Step-by-step explanation:

Total cards in the deck  = 20

Total prime numbered cards in deck  = { 2, 3, 5, 7, 11, 13, 17, 19}  = 8 cards

So, Probability of picking two prime cards from deck (without replacing)

= Probability of picking first prime card x Probability of picking second prime card

P( picking first prime card ) = $\frac{\textrm{Total prime cards in the deck}}{\textrm{Total available cards}}$

= $\frac{8 }{20} = \frac{2}{5}$

P( picking second prime card )  = $\frac{\textrm{Total prime cards in the deck}}{\textrm{Total available cards}}$

=$\frac{7}{19}$

Hence, the total probability =$\frac{2}{5} \times \frac{7}{19} = \frac{14}{95}$

or, B)  P(two prime numbers are drawn in a row) = 14/95