Problem Solving

On a biased die, an even number appears three times as frequently as an odd number. If the die is thrown twice, what is the probability that the sum is 10 or more?

1) 15/37 2) 17/72 3)35/72 4)23/37

Answer: [spoiler](2)[/spoiler]

Now a die has 3 odd nos 1,3,5 & 3 even 2,4,6

now even is three times more likely that odd

now we need to normalise the probabilties

we can say 3*3 + 1+1+1 =12 is the normalising factor (3:1 proportion)

i.e so P of 1,3,5 =1/12 & P of 2,4,6 = 3/12

so here the scenario's are

5,5 4,6 6,4 5,6 6,5 6,6

so reqd probabilty is

1/12 *1/12 + 3(3/12*3/12) + 2(1/12*3/12)

1/144 +27/144 + 6/144

=34/144

= 17/72

Ans B (2)