Determine the probabilities of the events in the following ( Hint: Use complemen
ID: 3146485 • Letter: D
Question
Determine the probabilities of the events in the following (Hint: Use complementary events.). Give solution rounded to the nearest hundredth. Explain Pleasea. Getting at least one sum of 4 or 9 on 3 rolls of a pair of dice.
The probability is
b. Getting a sum of 11 or greater at least once in 3 rolls of a pair of dice.
The probability is Determine the probabilities of the events in the following (Hint: Use complementary events.). Give solution rounded to the nearest hundredth. Explain Please
a. Getting at least one sum of 4 or 9 on 3 rolls of a pair of dice.
The probability is
b. Getting a sum of 11 or greater at least once in 3 rolls of a pair of dice.
The probability is
Explanation / Answer
a. A sum of 4 or 9 can appear as 2+2, 1+3, 3+1, 3+6, 6+3, 4+5, 5+4.
Altogether the probability of 4 or 9 appearing on one throw of a pair of dice is 7/36.
=> Probability that there won't be a sum of 4 or 9 in one throw = 1 - 7/36 = 29/36.
Probability that there won't be a sum of 4 or 9 on any of three throws = (29/36)3.
=> Probability that there will be atleast one sum of 4 or 9 in three throws = 1 - (29/36)3
= 0.48.
b. A sum of 11 or greater can only be obtained as 5+6, 6+5 or 6+6.
Probability of getting a sum of 11 or greater in one throw = 3/36 = 1/12.
=> Probability of not getting a sum of 11 or greater in one throw = 1 - 1/12 = 11/12.
Probability of not getting a sum of 11 or greater in three throws = (11/12)3.
=> Probability of getting atleast one sum of 11 or greater in three throws = 1 - (11/12)3 = 0.23.
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