Please help me to answer this. Thankyou and God bless!
asked Dec 13, 2016 in Statistics Answers by Kia

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:

To avoid this verification in future, please log in or register.

1 Answer

There are 4 suits so the chances of picking a spade initially are 1/4. There are 13 of each suit in a pack.

No spades: 39 other cards so if the first card is not a spade the probability is 39/52=3/4. Now there are 51 cards left, 13 of which are spades. The probability of no spade next is 38/51, then for the third card 37/50. The combined probability for no spades is 703/1700.

One spade: if a spade is drawn first the chances are 1/4. The next card is not a spade, chances are 39/51, and the third 38/50. Overall: 247/1700. Suppose the spade was drawn second: overall: 3/4 * 13/51 * 38/50=247/1700, and the same probability applies if the spade was third. So we have 3*247/1700=741/1700.

Two spades: this is similar to the non-spade being drawn in 1st, 2nd or 3rd position. We multiply one probability by 3. First two are spades: 1/4 * 12/51 * 39/50=39/850. Multiply by 3: 117/850.

Three spades: 1/4 * 12/51 * 11/50=11/850.

So we have:

#spades Probability

0             703/1700

1             741/1700

2             117/850

3               11/850

TOTAL:        1

answered Dec 13, 2016 by Rod Top Rated User (487,420 points)
Welcome to, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!
79,846 questions
83,680 answers
66,608 users