Assume that two fair dice are rolled. Answer the following questions. What is th
ID: 3825463 • Letter: A
Question
Assume that two fair dice are rolled. Answer the following questions. What is the probability that BOTH die land on 5? What is the probability that both numbers SUM to 5? What is the probability that the sum of the numbers is a multiple of 2 OR the sum is five or less? You have jar of coins. The jar contains 15 gold coins, 35 silver coins, and 10 copper coins. Answer the following questions If a coin is taken from the jar at random, what is the probability that it is gold? If a coin Is taken from the jar at random, what Is the probability that it is gold OR copper? Two coins are taken from the jar WITHOUT replacement What is the probability that both coins are silver?Explanation / Answer
solutions
1) two fair dice are rolled so total outcome will be = 62 =36.
P(E) =no. of favourable outcome /total outcome.
so P(both die land on 5) = 1/36
answer is 1/36
2) what is the probabilty that both number sum to 5?
total outcome =36
favourable outcome= {(1,4),(4,1),(2,3),(3,2)} = 4
P(E) =no. of favourable outcome /total outcome.
P(E) = 4/36 = 1/9
3)What is the probability that the sum of numbers is multiple of 2 OR the sum is five or less?
total outcome=36
(X) sum of number is multiple of 2 ={(1,3),(3,1),(2,2),(2,4),(2,6),(4,2),(6,2),(1,5),(5,1),(3,3),(3,5),(4,4),(4,6),(5,3), (5,5),(6,4),(6,6)}
=17/36
(Y) sum is less than or equal to 5 = {(1,1),(1,2),(1,3),(1,4),(2,1),(2,2),(2,3),(3,1),(3,2),(4,1)}
=10/36
(Z) sum is multiple of 2 and lessthan equal to 5 = {(1,3),(3,1),(2,2)}
=3/36
probablity = X+Y-Z
=17/36+10/36 -3/36
=24/36
=2/3
answer is 2/3
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4) if a coin is taken from the jar at random what is the probabilty that it is gold
we use combination here
formula=nCr= n ! / r! (n-r) !
total no. of coins =60
probabilty =15C1/60C1
=15/60
=1/4
answer is 1/4
5) if a coin is taken from the jar at random,what is the probabilty that it is gold or copper
probabilty =15C1/60C1 +10C1 / 60C1
= 15/60 + 10/60
=25/60
=5/12
answer is 5/12
6) two coins are taken from jar WITHOUT replacement.What is the probabilty that both coins are silver?
probabilty =35/60 *34/59
= 119/354