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057 - Problems on Probability

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Question:

1. If a pair of 6-sided dice are rolled, what is the probability of getting the sum of numbers as 5?
A 1/6
B 1/12
C 1/9
D 5/36

Feedback:

The no. of successful outcomes are 4 (1+4, 2+3, 3+2, 4+1). The total no. of likely outcomes is 36. Hence, probability = 4/36 = 1/9
Correct Answer: C
Your Answer:
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Question:

2. If three 6-sided dice are rolled, what is the probability of getting at least one 6?
A 1/6
B 125/216
C 3/6
D 91/216

Feedback:

Probability of NOT getting a six on each of the die is 5/6. Therefore probability of NOT getting a 6 at all is (5/6) X (5/6) X (5/6) = 125/216. Subtracting this no. from the total outcomes possible i.e. 216-125 = 91, the probability of getting at least one six is 91/216.
Correct Answer: D
Your Answer:
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Question:

3. If 3 cards are randomly chosen from a deck of 52 playing cards, what is the probability of getting all hearts?
A 1716/132600
B 3/52
C 1716/140608
D 2197/132600

Feedback:

As each card is drawn, the probability of getting another hearts diminishes in this order: 13/52, 12/51 ,11/50, 10/49 and so on. Hence, the probability of the event of getting 3 hearts is the product of the first three nos.
Correct Answer: A
Your Answer:
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Question:

4. If a card is randomly chosen from a deck of 52 playing cards, what is the probability of getting a hearts or a red?
A 39/52
B 1/2
C 1/4
D 38/52

Feedback:

Total no. of red cards = 26.
Total no. of hearts = 13
Since red cards include all the hearts as well, the favourable cards for the event are only 26. Therefore probability of getting a hearts or a red is 26/52 = 1/2. This is an example of non-mutually exclusive events.
Correct Answer: B
Your Answer:
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Question:

5. When two events, A and B, are mutually exclusive, the probability that A or B will occur is;
A P(A or B) = P(A) + P(B)
B P(A or B) = P(A) X P(B)

Feedback:

Probability of occurrence of a set of mutually exclusive events is the sum of the probability of each event.
Correct Answer: A
Your Answer:
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