A bag contains 9 counters. 4 of the counters are blue.
Two counters are taken out of the bag at random.
Calculate the probability that at least one of the two counters is blue.
Probability question?
2016-02-20 7:53 pm
回答 (6)
2016-02-20 8:01 pm
✔ 最佳答案
Well,P( at least 1 is blue ) = p10 + p01 + p11
where :
p11 : both are blue
p10 : 1st is blue not 2nd
p01 : 1st is NOT blue bot 2nd is (blue)
so
p11 = 4/9 * 3/8 = 12/72
p10 = 4/9 * 5/8 = 20/72
p01 = 5/9 * 4/9 = p10
so
P( at least 1 is blue ) = (20+20+12)/72
= 52/72
= 13/18
# 72.2%
hope it' ll help !!
2016-02-20 8:00 pm
B : take out a counter which is blue (number = 4)
N : take out a counter which is not blue (number = 5)
P(both the two counters are not blue)
= P(NN)
= (5/9) × (4/8)
= 5/18
P(at least one of the two counters is blue)
= 1 - P(both the two counters are not blue)
= 1 - (5/18)
= 13/18
N : take out a counter which is not blue (number = 5)
P(both the two counters are not blue)
= P(NN)
= (5/9) × (4/8)
= 5/18
P(at least one of the two counters is blue)
= 1 - P(both the two counters are not blue)
= 1 - (5/18)
= 13/18
2016-02-20 7:56 pm
the probability that at least 1 is blue=1- (probability that none are blue)
(5/9)(4/8)=5/18=prob that none are blue.
1-5/18= 13/18= probability that at least 1 is blue.
Hope this helps!
Edit: If the sample is with replacement, then the answer is 56/81. If its without replacement, then 13/18 is correct. Depends on replacement or not.
(5/9)(4/8)=5/18=prob that none are blue.
1-5/18= 13/18= probability that at least 1 is blue.
Hope this helps!
Edit: If the sample is with replacement, then the answer is 56/81. If its without replacement, then 13/18 is correct. Depends on replacement or not.
2016-02-20 9:21 pm
4C0x5C2/9C2= 5/18 not blue, 18/18-5/18=13/18 at least 1 blue. 13/18.
2016-02-20 7:58 pm
Assume that the 5 counters not blue are green
probability that at least one of the two counters is blue
= 1 - probability that the two counters are green
= 1 - 5C2/9C2
= 1 - (5!/3!2!)/(9!/2!7!)
= 1 - 15 / 36
probability that at least one of the two counters is blue
= 1 - probability that the two counters are green
= 1 - 5C2/9C2
= 1 - (5!/3!2!)/(9!/2!7!)
= 1 - 15 / 36
2016-02-20 7:54 pm
收錄日期: 2021-04-18 14:28:51
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