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Two dice are thrown simultaneously. The probability that at least one of them will have 6 facing up is
- a)1/36
- b)1/3
- c)25/36
- d)11/36
Correct answer is option 'D'. Can you explain this answer?
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Two dice are thrown simultaneously. The probability that at least one ...
P(atleast one of dice will have 6 facing
= 1 - P(none of dice have 6 facing up)
= 1 - P(none of dice have 6 facing up)
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Two dice are thrown simultaneously. The probability that at least one ...
Problem:
Two dice are thrown simultaneously. The probability that at least one of them will have 6 facing up is:
a) 1/36
b) 1/3
c) 25/36
d) 11/36
Solution:
To find the probability of at least one of the dice showing a 6, we can find the probability of the complement event and subtract it from 1.
Complement Event:
The complement event is the event where neither of the dice shows a 6.
Total Outcomes:
When two dice are thrown simultaneously, each die has 6 possible outcomes (numbers 1 to 6). Therefore, the total number of outcomes is 6 * 6 = 36.
Favorable Outcomes:
For the complement event to occur, both dice must show a number other than 6. So, each die has 5 favorable outcomes (numbers 1, 2, 3, 4, and 5). Therefore, the total number of favorable outcomes is 5 * 5 = 25.
Probability of Complement Event:
The probability of the complement event is the ratio of the number of favorable outcomes to the total number of outcomes. Therefore, the probability of the complement event is 25/36.
Probability of At Least One 6:
The probability of at least one of the dice showing a 6 is 1 minus the probability of the complement event. Therefore, the probability of at least one 6 is 1 - 25/36 = 11/36.
Hence, the correct answer is option d) 11/36.
Two dice are thrown simultaneously. The probability that at least one of them will have 6 facing up is:
a) 1/36
b) 1/3
c) 25/36
d) 11/36
Solution:
To find the probability of at least one of the dice showing a 6, we can find the probability of the complement event and subtract it from 1.
Complement Event:
The complement event is the event where neither of the dice shows a 6.
Total Outcomes:
When two dice are thrown simultaneously, each die has 6 possible outcomes (numbers 1 to 6). Therefore, the total number of outcomes is 6 * 6 = 36.
Favorable Outcomes:
For the complement event to occur, both dice must show a number other than 6. So, each die has 5 favorable outcomes (numbers 1, 2, 3, 4, and 5). Therefore, the total number of favorable outcomes is 5 * 5 = 25.
Probability of Complement Event:
The probability of the complement event is the ratio of the number of favorable outcomes to the total number of outcomes. Therefore, the probability of the complement event is 25/36.
Probability of At Least One 6:
The probability of at least one of the dice showing a 6 is 1 minus the probability of the complement event. Therefore, the probability of at least one 6 is 1 - 25/36 = 11/36.
Hence, the correct answer is option d) 11/36.
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