1. Two far dice are rolled. Find the probability that the numbers that appear A.
ID: 2903031 • Letter: 1
Question
1. Two far dice are rolled. Find the probability that the numbers that appear
A. are both 2;
B. have a total that is at most 10;
C. are both factors of 70 whose product divides 70;
D. add to a number that is divisible by 5.
2. Three dice are rolled. Find the probability that the numbers that appear
A. Are all multiples of 5;
B. Have a total that is at most 16;
C. Are three different primes;
D. Are all different.
3. A fair coin is tossed seven times. Find the probability of obtaining
A. Seven head;
B. Exactly five heads;
C. At most five heads;
D. At most one head;
E. An odd number of heads.
4. A basket contains five red balls, four white balls, and three blue balls. Two balls are drawn, one after the other, with the first ball replaced before the second is drawn. Find the probability of drawing
A. Two blue balls;
B. At most one blue ball;
C. At least one blue ball;
D. A blue ball and a white ball;
E. Either at least one blue ball or at least one white ball.
Explanation / Answer
1.
total numbers of outcomes when two dices are rolled = 6*6=36
A.
favourable outcome =(2,2)
number of favourable outcome =1
so
P=1/36
B.
three cases are avoided in which sum exceeds 10.those are (5,6),(6,5),(6,6)
P=33/36 = 0.916
C.
P=6/36 = 1/6
D.
P=7/36
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2.
total number of occurances =6*6*6=216
A.
P = 1/216
B.
P=212/216
C.
P=6/216 = 1/36
D.
P=120/216
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3.
total number of occurances = 2^7=128
A.
P=1/128
B.
P=21/128
C.
P=120/128
D.
P= 8/128
E.
P=64/128
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4.
IN this problem i am assuming that all balls of same colors are same.so
total number of occurances = 25+16+9+20+15+12=97
both red
both white
both blue
one red one white
one red one blue
one blue one white
A.
favourable =3*3=9
P=9/97
B.
favouable = 88
P=88/97
C.
P=36/97
D.
P=12/97
E.
P=84/97
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