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.

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 × ... .... .... .... ... ...

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 =  

probability = 0.000007122

85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560