Probability
Q. If a coin is flipped three times, what is the probability of getting exactly two heads?
A.
3/8
B.
1/2
C.
1/4
D.
1/8
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Solution
The total outcomes are 2^3 = 8. The combinations for exactly 2 heads are HHT, HTH, THH, which gives us 3 favorable outcomes. So, the probability is 3/8.
Correct Answer: A — 3/8
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Q. If a coin is tossed three times, what is the probability of getting at least one head?
A.
1/8
B.
1/2
C.
7/8
D.
3/8
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Solution
The probability of getting no heads (all tails) is (1/2)^3 = 1/8. Therefore, the probability of getting at least one head is 1 - 1/8 = 7/8.
Correct Answer: C — 7/8
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Q. If a coin is tossed three times, what is the probability of getting exactly two heads?
A.
3/8
B.
1/2
C.
1/4
D.
5/8
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Solution
The number of ways to get exactly 2 heads in 3 tosses is 3 (HHT, HTH, THH). The total outcomes are 2^3 = 8. So, the probability is 3/8.
Correct Answer: A — 3/8
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Q. In a class of 30 students, 18 are girls. If a student is chosen at random, what is the probability that the student is a boy?
A.
1/3
B.
2/5
C.
1/2
D.
3/5
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Solution
The number of boys is 30 - 18 = 12. The probability is 12/30 = 2/5.
Correct Answer: A — 1/3
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Q. In a class of 30 students, 18 are girls. If a student is selected at random, what is the probability that the student is a boy?
A.
0.4
B.
0.6
C.
0.5
D.
0.3
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Solution
The number of boys is 30 - 18 = 12. The probability is 12/30 = 0.4.
Correct Answer: B — 0.6
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Q. In a lottery, there are 10 tickets, and 3 of them are winning tickets. What is the probability of picking a winning ticket?
A.
1/10
B.
1/3
C.
3/10
D.
1/5
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Solution
The probability of picking a winning ticket is 3/10.
Correct Answer: C — 3/10
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Q. In a lottery, there are 100 tickets, and 10 of them are winning tickets. What is the probability of picking a winning ticket?
A.
1/10
B.
1/5
C.
1/20
D.
1/50
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Solution
The probability of picking a winning ticket is 10/100 = 1/10.
Correct Answer: B — 1/5
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Q. Two coins are tossed. What is the probability of getting at least one head?
A.
1/4
B.
1/2
C.
3/4
D.
1/3
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Solution
The possible outcomes are HH, HT, TH, TT. The outcomes with at least one head are HH, HT, TH. So, the probability is 3/4.
Correct Answer: C — 3/4
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Q. Two dice are rolled. What is the probability that the sum of the numbers on the dice is 7?
A.
1/6
B.
1/12
C.
1/36
D.
5/36
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Solution
The combinations that give a sum of 7 are (1,6), (2,5), (3,4), (4,3), (5,2), (6,1). There are 6 combinations out of 36 total outcomes, so the probability is 6/36 = 1/6.
Correct Answer: D — 5/36
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