Question

A and B each throw a die. The probability that A's throw is not greater than B's is

• A. $\frac{21}{36}$
• B. $\frac{12}{35}$
• C. $\frac{7}{12}$
• D. $\frac{5}{12}$

Answer 1

The correct option is C $\frac{7}{12}$

A and B throws a die

Ways that B's throw always greater than A's is

If A=1 then B=1,2,3,4,5,6 P1=1/6*6/6

If A=2 then B=2,3,4,5,6 P2=1/6*5/6

If A=3 then B=3,4,5,6 P3=1/6*4/6

If A=4 then B=4,5,6 P4=1/6*3/6

If A=5 then B=5,6 P5=1/6*2/6

If A=6 then B=6 P6=1/6*1/6

Total probability=1/6(1/6+2/6+3/6+4/6+5/6+6/6 )=1/36(1+2+3+4+5+6)

=1/36*21=7/12