When tossing a pair of dice simultaneously, what is the likelihood that the sum of the resulting numbers equals 8?
Show answer Hide answer
Answer: A. 5/36
Explanation
The correct answer is five over thirty-six for the probability of rolling a sum of eight. There are thirty-six total possible outcomes when tossing a pair of standard dice. Five specific outcome pairs sum to eight, creating the fraction five over thirty-six. Each die has six faces, yielding six multiplied by six total sample space outcomes. The favorable outcome pairs are two and six, three and five, four and four, five and three, six and two. Probability equals the number of favorable outcomes divided by total possible outcomes.
Probability calculations for dice rolls form the foundation of games of chance and board games. Statistical modeling uses discrete sample spaces to analyze random event likelihoods. Actuarial science applies combinatorial probability principles to assess insurance risk factors. Option B represents four favorable outcomes, missing one valid pair combination. Option C simplifies the fraction incorrectly to one-twelfth instead of five thirty-sixths. Option D overestimates the probability by confusing sample space counts with outcomes.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
Related questions
Q1. Out of 120 pupils in a class, 45 attained a B grade. What percentage achieved a B grade?
Show answer Hide answer
Answer: C. 37.5%
Forty five students attained a B grade out of a total class population of one hundred twenty. Dividing forty five by one hundred twenty gives the decimal fraction equivalent of zero point three seven five. Multiplying by...
Q2. Pipes P and Q fill a cistern in 18 and 24 minutes respectively. With both open initially, when must the first pipe be closed so the cistern fills in exactly 12 minutes?
Show answer Hide answer
Answer: B. after 9 mins
Pipe Q works for the entire 12 minutes to help fill the cistern completely. Pipe P contributes to the filling process for only the first 9 minutes of operation. Combining the fractional work completed by both pipes equal...
Q3. The H.C.F of 3240, 3600 and a third integer is 36, and their L.C.M is 24 * 35 * 52 * 72. Find the third number___________?
Show answer Hide answer
Answer: A. 22 * 35 * 72
The highest common factor divides evenly into all given integers, providing the baseline common prime factors. The least common multiple contains the highest exponents of all prime factors present across the integer set....
Q4. One valve fills a cistern in 2 hours while a second drains it in 3 hours. How long will filling take if both remain open?
Show answer Hide answer
Answer: B. 6 Hours
The first valve fills one half of the cistern per hour while the second drains one third per hour. Subtracting the draining rate from the filling rate gives a net fill rate of one sixth per hour. Inverting the net fill r...
Q5. P takes twice as long as Q or thrice as long as R to complete a task. Working together, they finish it in 2 days. How long will Q take working independently?
Show answer Hide answer
Answer: D. 6
The combined working rate of all three participants equals one half per day. Relating individual speeds reveals that Q completes the task in exactly six days. Working together accelerates the completion time significantl...
Q6. Integers x and y satisfy 3 1/x * y 2/5 = 13 3/4 in lowest terms, where x = ? and y = ____________?
Show answer Hide answer
Answer: D. x = 8, y = 4
Converting mixed numbers into improper fractions simplifies algebraic expressions involving unknown variables. Equating the numerator and denominator products from both sides isolates the variables x and y. Solving the r...