Question

A student made a cube-shaped die from a card sheet. Instead of writing numbers 1,2,3,4,5,6 on its face, he wrote letters a,b,c,d,e,f one on each face randomly. If he rolls the die twice, find the probability that he gets a vowel on the upper face both times​.

Answer 1

A student made a cube-shaped die from a card sheet. Instead of writing numbers 1,2,3,4,5,6 on its face, he wrote letters a,b,c,d,e,f one on each face randomly. So, he rolls the dice twice.

∴ S = {aa, ab, ac, ad, ae, af, ba, bb, bc, bd, be, bf, ca, cb, cc, cd, ce, cf, da, db, dc, dd, de, df,  ea, eb, ec, ed, ee, ef, fa, fb, fc, fd, fe, ff}

∴ n(S) = 36

Let A be the vowel on the upper face both times

A = {aa, ae, ea, ee}

∴ n(A) = 4

∴ P(A) = `("n"("A"))/("n"("S")) = 4/36 = 1/9`