Question

An experiment consists of drawing 10 cards from an ordinary 52-card pack. (a) If the drawing is done with replacement, find the probability that no two cards will have the same face value. (b) If the drawing is done without replacement, find the probability that at least 9 cards will be of the same suit.

Answer 1

Answer:

Probability = 0.0073

probability = 0.000007122

Step-by-step explanation:

given data

drawing = 10 cards

ordinary -card pack  = 52  pack

solution

we know that here drawings done with replacement so that there is Probability that not 2 card of the same denomination

so

Probability = Probability of selecting a card × Probability of selecting a card not of the first denomination × Probability of drawing a card not from 2 denominations and continuous so on .......

so

Probability = 1 × $\frac{52-4}{52} \times \frac{52-8}{52}$ ... .... .... .... ... ...

Probability = 0.0073

and

when cards is drawn without replacement

probability = probability that exactly 9 of same suit and 10th of a different suit + Probability all 10 are of same suit  

so

probability = $\frac{\frac{4}{1}\times \frac{13}{9}\times \frac{52-13}{1} + \frac{4}{1} \times \frac{13}{10} }{\frac{52}{10} }$  

probability = 0.000007122