consider selecting 6 cards from a pack of cards without replacement what is the probability that 3 of the cards will be black
Answers
Explanation:
no of favourable item upon total no of item
=3upon6
=1upon2
Concept
Probability is the likeliness of happening an event among all the events possible. The formula of calculating probability of an event is as under:
Probability= Number of outcomes/ total events.
To find
The probability of having 3 black cards if 6 are drawn.
Explanation
Total cards available=52
Number of red cards=26
Number of black cards=26
Total ways of selecting 6 cards out of 52 cards=52 C 6
Total ways of selecting 3 cards out of 26 black cards =26 C 3.
So the probability is (26C3*26C3)/52C6
={26!/3!(26-3)!*26!/3!(26-3)!}/52!/6!(52-6)!
={(26*25*24)/3*2*1} *{26*25*24/3*2*1}/(52*51*50*49*48*47/6*5*4*3*2*1)
=15600/6 * 15600/6 /14658134400/720
=2600*2600/20358520
=6760000/20358520
=0.332
Hence the probability of selecting 3 blacks from 6 cards drawn is 0.332.
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