62 470
Assignments Done
98,8%
Successfully Done
In June 2018

Answer to Question #23921 in Statistics and Probability for umesh jha

Question #23921
two cards are drawn from a well shuffled pack of 52 cards and thrown away. find the probability of drawing an ace from the remaining 50 cards
Expert's answer
According to the total probability formula, we have

P(draw an ace from the remaining 50 cards) =

P(draw an ace | two drawn cards were aces) * P(draw two aces from 52 cards) +

P(draw an ace | two drawn cards were ace and not an ace) * P(draw one ace and one not ace from 52 cards) +

P(draw an ace | two drawn cards were not aces) * P(not to draw two aces from 52 cards).

Obviously,

P(draw an ace | two drawn cards were aces) = 0,

P(draw an ace | two drawn cards were ace and not an ace) = 3/50,

P(draw an ace | two drawn cards were not aces) = 4/50,

and

P(draw two aces from 52 cards) = 4/52 * 3/51,

P(draw one ace and one not ace from 52 cards) = 4/52 * (1 - 3/51) (or, equally, (1-4/52) * 4/51),

P(not to draw two aces from 52 cards) = (1 - 4/52)(1 - 4/51) (or, equally, 1 - 4/52 * 3/51).

So,

P(draw an ace from the remaining 50 cards) =

0 * 4/52 * 3/51 + 3/50 * 4/52 * (1 - 3/51) + 4/50 * (1 - 4/52)(1 - 4/51) =

= 3/50 * 4/52 * 48/51 + 4/50 * 48/52 * 47/51 = 9024/132600 = 1128/16575 ≈ 0.068.

Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be first!

Leave a comment

Ask Your question

Submit
Privacy policy Terms and Conditions