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A set consists of consecutive integers from 11 to 35 . Wh
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23 Feb 2020, 09:37
23 Feb 2020, 09:37
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50% (01:38) correct
50% (01:56) wrong based on 22 sessions
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A set consists of consecutive integers from 11 to 35. What is the probability that the product of two numbers, picked from this set one after the other without replacement, is an even number?
a. 13/50
b. 17/50
c. 23/50
d. 37/50
e. 41/50
a. 13/50
b. 17/50
c. 23/50
d. 37/50
e. 41/50
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: A set consists of consecutive integers from 11 to 35 . Wh
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23 Feb 2020, 10:18
23 Feb 2020, 10:18
1
Asif123 wrote:
A set consists of consecutive integers from 11 to 35. What is the probability that the product of two numbers, picked from this set one after the other without replacement, is an even number?
a. 13/50
b. 17/50
c. 23/50
d. 37/50
e. 41/50
a. 13/50
b. 17/50
c. 23/50
d. 37/50
e. 41/50
There are 25 integers from 11 to 35 inclusive
13 of those integers are ODD, and 12 are EVEN
There are three different ways to get an even product:
1) 1st # is even and 2nd # is even
2) 1st # is even and 2nd # is odd
3) 1st # is odd and 2nd # is even
So, we get...
P(product is even) = P(1st # is even AND 2nd # is even OR 1st # is even AND 2nd # is odd OR 1st # is odd AND 2nd # is even)
= P(1st # is even AND 2nd # is even) + P(1st # is even AND 2nd # is odd) + P(1st # is odd AND 2nd # is even)
= [P(1st # is even) x (2nd # is even)] + [P(1st # is even x P(2nd # is odd)] + [P(1st # is odd) x P(2nd # is even)]
= [12/25 x 11/24] + [12/25x 13/24)] + [13/25 x 12/24]
= 11/50 + 13/50 + 13/50
= 37/50
Answer: D
Cheers,
Brent
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: A set consists of consecutive integers from 11 to 35 . Wh
[#permalink]
23 Feb 2020, 10:21
23 Feb 2020, 10:21
1
Asif123 wrote:
A set consists of consecutive integers from 11 to 35. What is the probability that the product of two numbers, picked from this set one after the other without replacement, is an even number?
a. 13/50
b. 17/50
c. 23/50
d. 37/50
e. 41/50
a. 13/50
b. 17/50
c. 23/50
d. 37/50
e. 41/50
Here's a faster solution....
There are 25 integers from 11 to 35 inclusive
13 of those integers are ODD, and 12 are EVEN
P(product is even) = 1 - P(product is NOT even)
= 1 - P(product is ODD)
P(product is ODD) = P(1st # is odd AND 2nd # is odd)
= P(1st # is odd) x P(2nd # is odd)
= 13/25 x 12/24
= 13/50
So, P(product is even) = 1 - 13/50 = 37/50
Answer: D
Cheers,
Brent
